QUESTION 1
[tex]cos\ \theta = \frac{12}{13}\\\theta = cos^{-1}\frac{12}{13} = 22.62\textdegree = 0.3948\ (\text{radians})[/tex]
QUESTION 2
[tex]\frac{3\pi}{2} < \theta < 2\pi\ \text{then find}\ sin(2\theta)[/tex]
First, the fact that we have [tex]sin(2\theta)[/tex] means we have to adjust our range
[tex]\frac{3\pi}{2} < \theta < 2\pi\ \ \text{becomes}\ \ 3\pi < 2\theta < 4\pi\[/tex]
[tex]sin\ 2\theta = \frac{3\pi}{2}\\2\theta = sin^{-1} \frac{3\pi}{2}\\2\theta = \text{error}[/tex]
There are no solutions to inverse sin of [tex]\frac{3\pi}{2}\\[/tex]
HELP PLEASEEEEEEEEEEEe
Answer:X + (2 and 1/2) - 3/4 = 5 and 1/4
X + 2 and 2/4 - 3/4 = 5 and 1/4 <--- common denominator
X + 10/4 - 3/4 = 21/4
X + 7/4 = 21/4
X = 21/4 - 7/4 = 14/4 = 7/2 = 3 and 1/2
There are yellow counters and black counters in a bag in the ratio 3:1
21 yellow counters are removed and the ratio becomes 5:4
Work out how many black counters there are in the bag.
Answer:
12 black countersStep-by-step explanation:
Let the yellow counters be represented by 'y' and black counters by 'b'.
Originally
y : b = 3 : 1After removing 21 counters
y - 21 : b = 5 : 4Taking the first ratio, equate it to b.
y/b = 3b = y/3Now, substitute for 'b' in the second ratio.
y - 21 / (y/3) = 5/43 (y - 21) / y = 5/412 (y - 21) = 5y12y - 252 = 5y7y = 252y = 36 yellow countersNow, to find b :
b = y/3b = 36/3b = 12 black countersAnswer:
12
Step-by-step explanation:
Given ratio
yellow : black = 3 : 1
⇒ yellow : black = [tex]3x : x[/tex]
If 21 yellow counters are removed and the ratio becomes 5 : 4
[tex]\implies \textsf{yellow - 21: black = 5 : 4}[/tex]
[tex]\implies (3x - 21):x=5:4[/tex]
[tex]\implies \dfrac{3x - 21}{x}=\dfrac54[/tex]
[tex]\implies 4(3x - 21)=5x[/tex]
[tex]\implies 12x-84=5x[/tex]
[tex]\implies7x=84[/tex]
[tex]\implies x=12[/tex]
Substituting [tex]x=12[/tex] into the original ratio:
[tex]\implies \textsf{yellow : black} =3(12) : (12)=36:12[/tex]
So the total number of black counters = 12
I am a teacher and need to proofread my student's work. But it makes it quite hard when I need to watch a 30-second ad to make sure their answers are right. Is there any way I can bypass this without having to pay because this is a huge inconvenience?
Answer:i dont think so..
Step-by-step explanation:
I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
119
Step-by-step explanation:
all angles in a triangle add up to 180
180-61-58=61
so missing inner angle is 61
then to solve 1:
180-61=119
A solid box with height 90cm, width 70cm and length 90cm needs to be painted.
The paint costs £0.02 per cm2.
How much will it cost to paint the outside of the box?
Answer:
£828
Step-by-step explanation:
The first step to solve this problem is to find the surface area of the solid box. The formula for surface area for a rectangular prism is [tex]2(wl+hl+hw)[/tex]where w is width, l is length, and h is height. Plugging values in gives [tex]2(90*90+70*90+70*90)=41400[/tex] cm^2.
Because each cm^2 of paint costs £0.02, a ratio can be created.
[tex]\frac{1}{0.02} =\frac{41400}{x}[/tex]
Cross multiplying gives: [tex]x=828[/tex], so to paint the whole outside of the box, it would cost £828.
A bag has 1 red marble, 4 orange marbles, 2 green marbles, 6 blue
4
marbles, and 5 black marbles. You randomly pull a marble from the
bag, put it back, and then pull out another one.
What is the probability of not getting a black and then not getting a
green? Write your answer as a fraction.
Step-by-step explanation:
so first you must calculate the total amount of marbles there are, that being addition : 1+4+2+6+4+5 = 24 in total. now you want to make that into a fraction, 24/24 marbles, once again all together, so the probability of not getting a black marble is 5/24 and probability of not getting a green is 2/24.
How much sugar is in 200 grams of 5% sugar syrup
Answer:
10 grams
Step-by-step explanation:
200 x 5 = 1000
If we move the decimal over two places left we get :
10.00
That means that there are 10 grams of sugar in 200 grams of 5% sugar syrup
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Have a nice day.
Question 2 of 21
In Accra, 30% of workers owns a car. In a sample of 10 workers, what is the probability that exactly three workers owns a car?
O A. 0.267
OB. 0.65
O C. 0.48
O D.0.73
Using the binomial distribution, it is found that the probability that exactly three workers owns a car is given by:
A. 0.267.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
30% of workers owns a car, hence p = 0.3.A sample of 10 workers is taken, hence n = 10.The probability that exactly three workers owns a car is given by P(X = 3), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.267[/tex]
Hence option A is correct.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
John made a lump sum deposit of $ 7,800 in an account that pays 5.5% per year. Find
the value (maturity value) of his account after 3 years. How much is the interest ?
Maturity Value: 9,159.08
Interest: 1,359.08
f(n)=−48⋅(-¼)^n. Complete the recursive formula of f(n)
f(1)=
f(n)=f(n-1)⋅
The function f(n)=−48⋅(-¼)^n is a geometric sequence
The recursive definition of f(n) is f(1) = 12; f(n) = f(n - 1) . -¼
How to determine the recursive formula of f(n)The function is given as:
f(n)=−48⋅(-¼)^n
Calculate f(1)
f(1)=−48⋅(-¼)^1
This gives
f(1) = 12
Calculate f(2)
f(2)=−48⋅(-¼)^2
This gives
f(2) = -3
Calculate the common ratio (r)
r = f(2)/f(1)
So, we have:
f = -3/12
Simplify
r = -1/4
Recall that: r = f(2)/f(1)
This gives
-1/4 = f(2)/f(1)
Make f(2) the subject
f(2) = -1/4* f(1)
Express 1 as 2 - 1
f(2) = -1/4* f(2 - 1)
Substitute 2 for n
f(n) = -1/4* f(n - 1)
Rewrite as:
f(n) = f(n - 1) . -¼
Hence, the recursive definition of f(n) is f(1) = 12; f(n) = f(n - 1) . -¼
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Pls help easy math 2 pics
Answer:
in the problem 17 the answer is 30 becase you times 6 and 6 and you git 30.problem 18 you do the same thing
Step-by-step explanation:
hope this helps if not let me now
Find the area of the shaded region
Answer:
20.52 cm²
Step-by-step explanation:
[tex]\textsf{Area of a semicircle}=\sf \dfrac12\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Area of a triangle}=\sf \dfrac12bh \quad \textsf{(where b is the base and h is the height)}[/tex]
Given:
[tex]\pi[/tex] = 3.14r = 6 cmb = 12 cmh = 6 cm[tex]\begin{aligned}\implies \textsf{Shaded area} & =\sf \dfrac12\pi r^2-\sf \dfrac12bh\\ & = \sf \dfrac12 \cdot 3.14 \cdot 6^2-\dfrac12 \cdot 12 \cdot 6\\ & = \sf 56.52-36\\ ^& = \sf 20.52\:\:cm^2\end{aligned}[/tex]
Answer:
20.52cm^2
Step-by-step explanation:
from the picutre we can see that this is a semicircle with 2 right angle triangles inside it. to find the area we will solve for the semi circle then solve for the triangles and and subtract
circle area is [tex]\pi r^{2}[/tex] leaving the semicircle to be [tex]\frac{\pi r^{2} }{2}[/tex] for the semi circle
next we need the radius. since the diameter is given, we can solve for r by dividing it in two
12 ÷ 2 = 6
so the area of the semi circle is [tex]\frac{\pi 6^{2} }{2}[/tex]
this gives 18[tex]\pi[/tex]cm^2 if we simplify
next the triangles, since they are equal in size we can treat them as a square and stack them. this is because they have equal side lengths so when stacked they form a square:
base x height divided by 2 times 2 would be the normal process to find two equal triangles but you can see the division and multiplication cancel out
6x6= 36cm^2
finally subtracting the areas to find the shaded region and use 3.14 as pi
18[tex]\pi[/tex]cm^2 - 36cm^2 = 20.52cm^2
NO LINKS!!!
Movies generally lose 23% of it's audience for each week in the theatre. A movie STARTED with an audience of 196 people per viewing.
Answers:
a) The equation is [tex]y = 196(0.77)^x[/tex]
b) See image attachment below
c) See image attachment below
d) Week 10
=======================================================
Explanation:
a)
One common template for an exponential equation is [tex]y = a*b^x[/tex] where 'a' is the starting amount and b is the growth or decay factor.
a = 196 is the starting amount of people who saw the movie per showtime
b = 1-0.23 = 0.77 is the decay factor. If the view count goes down by 23%, then we keep the remaining 77%
Therefore we go from [tex]y = a*b^x[/tex] to [tex]y = 196(0.77)^x[/tex]
x = number of weeks
y = number of people, per viewing, who saw the movie for the particular week
--------------------
b)
Plug in x = 0 to find that y = 196
Plug in x = 1 to get y = 150.92 which rounds to y = 151 since we're talking about the number of people
Repeat for x = 2 all the way up to x = 9 to account for the first ten weeks. We stop at 9 instead of 10 because we started at x = 0.
The table is shown in the attachment below next to the graph.
I'm not sure why your teacher put a dollar sign over the second column of the table when it should be the number of people. It might be a typo. If they meant to do it, then there's missing information about ticket prices.
--------------------
c)
The graph is shown below. You can plot each (x,y) point on the same grid and then draw a curve through them. A much quicker way is to use software like GeoGebra (which is what I used) or Desmos or a pocket calculator. There are tons of many options to pick from. Feel free to choose your favorite.
The blue dashed segments on the graph visually help verify the result of part (d). We have y = 20 lead to an x value somewhere between x = 8 and x = 9. When submitting the graph to your teacher, you'll leave out the blue dashed segments.
--------------------
d)
Refer to the table we made in part (b). We have x = 9 lead to y = 19 approximately which is when y is below 20 people. Recall that x = 0 refers to week 1, so x = 9 refers to week 9+1 = 10. Week ten is where the view count drops below 20 people per showing.
If you wanted to use the graph in part (c), then you'd follow the blue dashed line mentioned earlier. Start at the y axis at y = 20. Trace the blue dashed line until reaching the curve. Then drop straight down to arrive somewhere between x = 8 and x = 9. Round up to x = 9. Then make the adjustment to go from x = 9 to week ten.
If you want an algebraic method, then follow the steps below.
Plug in y = 20 and solve for x. We'll need to involve logarithms to isolate the exponent.
[tex]y = 196(0.77)^x\\\\20 = 196(0.77)^x\\\\20/196 = (0.77)^x\\\\0.1020408 \approx (0.77)^x\\\\(0.77)^x \approx 0.1020408\\\\\text{Log}\left((0.77)^x\right) \approx \text{Log}(0.1020408) \\\\x*\text{Log}\left(0.77\right) \approx \text{Log}(0.1020408) \\\\x \approx \text{Log}(0.1020408)/\text{Log}\left(0.77\right) \\\\x \approx 8.7325564 \\\\[/tex]
This rounds up to x = 9 leading to week ten as the answer.
As confirmation
[tex]y = 196(0.77)^x = 196(0.77)^8 \approx 24.22 \approx 24\\\\y = 196(0.77)^x = 196(0.77)^9 \approx 18.65 \approx 19\\\\[/tex]
Answer:
Part (a)We can model this as an exponential equation.
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is growth factorx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
As the movie theatre lost 23% of its audience each week, the growth (decay) factor will be 100% - 23% = 77% → 0.77
Given:
a = 196b = 0.77x = times (in weeks)y = audience (in number of people)Substitute the given values into the formula to create the exponential equation:
[tex]y=196(0.77)^x[/tex]
Part (b)[tex]\begin{tabular}{| c | r |}\cline{1-2} \bf weeks & \bf audience \\\cline{1-2} 1 & 150.92\\\cline{1-2} 2 & 116.21\\\cline{1-2} 3 & 89.48\\\cline{1-2} 4 & 68.90\\\cline{1-2} 5 & 53.05\\\cline{1-2} 6 & 40.85\\\cline{1-2} 7 & 31.46\\\cline{1-2} 8 & 24.22\\\cline{1-2} 9 & 18.65\\\cline{1-2} 10 & 14.36\\\cline{1-2}\end{tabular}[/tex]
**all values rounded to 2 dp**
Part (c)see attached for graph
Part (d)Set y < 20 and solve for x:
[tex]\begin{aligned}196(0.77)^x & < 20\\\\(0.77)^x & < \dfrac{5}{40}\\\\\ln (0.77)^x & < \ln\left(\dfrac{5}{49}\right)\\\\x\ln (0.77) & < \ln\left(\dfrac{5}{49}\right)\\\\x & > \dfrac{\ln\left(\dfrac{5}{49}\right)}{\ln (0.77)}\\\\x & > 8.732555795\end{aligned}[/tex]
Therefore, the movie audience will fall below 20 people per viewing during the 9th week.
PLEASE HELP PLEASE PLEASE HELP
Answer:
Step-by-step explanation:
the median is 26.5, but rounding that up the median will be 27. you can find this by determining the middle number of the data set.
a rectangular prism has length x, width x/2 and height x/3. Which expression represents the volume of the prism?
Answer:
x^3 / 6
Step-by-step explanation:
Multiply the three dimensions to get the volume
x * x/2 * x/3 =
The expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that, the length is x, width x/2, and height is x/3.
The volume of the rectangular prism is the product of the length, width, and height.
V= length × width × height
V=x × x/2 × x/3
Apply the multiplication operation in the fraction
Simply multiply the numerators to obtain the product's numerator and the denominators to obtain the product's denominator in order to multiply two fractions.
V=x³/6
Thus, the expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.
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If you roll a 6-sided die 54 times, what is the best prediction possible for the number of times
you will roll a five?
The following chart shows a company's sales records of four employees over the past year,
Sales by Month
50
45
40
Sales 61000)
35
Ben
Marcel
30
25
Rebecca
20
2
8 9 10 11 12
Month
Based on this graph, which employee is likely to have the greatest sales next month?
a Ben
b Marcel
c Kim
d. Rebecca
Save and Exit
Next
Sul
Mark this and return
Answer:
The answer is C
Step-by-step explanation:
Please help me answer this
Answer:
option A is the correct answer
solve for x :)
i’m not sure how to solve this it’s from geometry lesson 10.2
Step-by-step explanation:
Angle of a circle = 360
x + 90 + 84 + 16 = 360
x + 190 = 360
x = 170°
Can U Guys Tell Me The Angle And Type?
Answer:
The angle is 90°, and the type of angle is a right angle.
Step-by-step explanation:
That is a right angle, the little box and the straight lines indicate that is one. A right angle will always be 90°.
The distance between second base and third base on a regulation baseball field is 30 yards. Choose the word and number to complete the sentence correctly. To convert 30 yards to feet
Answer:
To convert 30 yards to feet, multiply by 3.
Step-by-step explanation:
We have to find out how many feet is in 1 yard and we have to multiply by 3 to find the answer. So the answer is multiply by 3
Its a multiple choice, HELP IM BEGGING
Answer:
B)
E)
Step-by-step explanation:
translation Dilation
M(x,y) ——————>M”(x”,y”)=(x+5,y+8) ——————> M’(x’,y’)=(3x”,3y”)
S(-5,-8) ——————>S”(x”,y”)=(0,0) ——————> S’(x’,y’)=(0,0)
R(-7,-6) ——————>R”(x”,y”)=(-2,2) ——————> R’(x’,y’)=(-6,6)
Q(-8,-10) ——————>Q”(x”,y”)=(-3,-2) ——————> Q’(x’,y’)=(-9,-6)
There are 165 concrete blocks available to make a retaining wall. The bottom 3
rows will all have the same number of blocks. The next six rows will each have 2
blocks fewer than the row below it. How many blocks are in each row?
Answer:
12
Step-by-step explanation:
The number of blocks in each row, from bottom to top, is: 23, 23, 23, 21, 19, 17, 15, 13, 11.
Step 1: Let's assume the number of blocks in each row of the bottom 3 rows is "x."
Step 2: The next six rows will each have 2 blocks fewer than the row below it. So, the number of blocks in each of these rows can be represented as:
x - 2, x - 4, x - 6, x - 8, x - 10, x - 12.
Step 3: Now, we can calculate the total number of blocks in all the rows.
For the bottom 3 rows, there are a total of 3 * x = 3x blocks.
For the next six rows, there are a total of (x - 2) + (x - 4) + (x - 6) + (x - 8) + (x - 10) + (x - 12) = 6x - 42 blocks.
Step 4: The total number of blocks in the wall is given as 165 blocks. So, we can set up an equation:
3x + 6x - 42 = 165
Step 5: Now, solve for x:
9x - 42 = 165
9x = 165 + 42
9x = 207
x = 207 / 9
x = 23
Step 6: Now that we have the value of x, we can find the number of blocks in each row:
The bottom 3 rows: x = 23 blocks each.
The next six rows:
x - 2 = 23 - 2
= 21 blocks,
x - 4 = 23 - 4
= 19 blocks,
x - 6 = 23 - 6
= 17 blocks,
x - 8 = 23 - 8
= 15 blocks,
x - 10 = 23 - 10
= 13 blocks,
x - 12 = 23 - 12
= 11 blocks.
So, the number of blocks in each row, from bottom to top, is: 23, 23, 23, 21, 19, 17, 15, 13, 11.
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Which of the following ordered pairs is represented by a point located on the x-axis?
(-3, -3)
( - 6,6)
(5,0)
(0,5)
Answer:
(5,0)
Step-by-step explanation:
The # 5 is on the x axis and there is no value for the y since it is 0. This means that this ordered pair will be located on the x-axis.
kawika is a woodworker and he carves a block in the shape of a right triangular prism. what is the total surface area of the block
Answer:The answer is D
Step-by-step explanation:
I know this because all the area of each face is equal to 10+10+52+32+40 and that is equal to 144in. squared
Answer:
D :)
Step-by-step explanation:
wait, have you smiled today? its very important:)
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS IF YOU DO THEN YOU GET REPORTED AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answer:
Angle A=60
Step-by-step explanation:
If ABC is approximately equal to DEF, A=D.
So x+30=2x
x+30=2x -> 30=x
If A=x+30 and x=30 then 30+30=60.
Please help me outttt
Answer:
2 + [tex]\sqrt{3}[/tex]
Step-by-step explanation:
In decimal form, it is also 3.73205080...
hope this helps :)
9. The price of one gallon of heating oil is $2.689.Which is this number rounded
to the nearest penny?
A $2.68
B $2.69
C $2.70
D $3.00
Solve the equation for x.
X-7 = 7
Enter the number that belongs in the green box.
x = [?]
Answer:
14
Step-by-step explanation:
1. Add 7 to both sides
2. This leaves us with x=14
Help Me on this!!
[tex] \\ \\ [/tex]
So here we are given that a || b and c || d, so the quadrilateral formed by the intersection of the four lines is just a parallelogram, so recall the property of parallelogram that parallelogram's opposite angles are always equal and the interior angles on the same side add up to 180°, and the property of angles that the alternate angles are always equal (that's angles Like in the Shape Z) and vertically opposite angles are equal (like in shape of X) and the property of linear pair i.e the sum of all angles on a plane line is 180°.
Now, as angles 3 and 7 are on a line d, so their sum will just be 180°, by property of linear pair
[tex]{:\implies \quad \sf m\angle 3+m\angle 7=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 7+74^{\circ}=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 7=180^{\circ}-74^{\circ}}[/tex]
[tex]{:\implies \quad \boxed{\bf{m\angle 7=106^{\circ}}}}[/tex]
Also, as angles 8 and 3 are vertically opposite angles, so they will be same, so we have
[tex]{:\implies \quad \boxed{\bf{m\angle 8=74^{\circ}}}}[/tex]
Now also, angle 7 and angle 11 are opposite angles of the parallelogram, so they will be equal, so we have :
[tex]{:\implies \quad \boxed{\bf{m\angle 11=106^{\circ}}}}[/tex]
Also, the interior angles on same side of Parallelogram add upto 180°, so we can have ;
[tex]{:\implies \quad \sf m\angle 11+m\angle 13=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 13+106^{\circ}=180^{\circ}}[/tex]
[tex]{:\implies \quad \sf m\angle 13=180^{\circ}-106^{\circ}}[/tex]
[tex]{:\implies \quad \boxed{\bf{m\angle 13=74^{\circ}}}}[/tex]
Also, Opposite angles of Parallelogram are equal, so angle 6 will be equal to angle 13, so angle 6 will be 74° and we also know the Vertically Opposite angles are equal. So, for angle 1 we have
[tex]{:\implies \quad \boxed{\bf{m\angle 1=74^{\circ}}}}[/tex]
Now, we are end with the conclusion :
[tex]{\bf{m\angle 1=74^{\circ}}}[/tex][tex]{\bf{m\angle 7=106^{\circ}}}[/tex][tex]{\bf{m\angle 8=74^{\circ}}}[/tex][tex]{\bf{m\angle 11=106^{\circ}}}[/tex][tex]{\bf{m\angle 13=74^{\circ}}}[/tex][tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Measure of Angle 3 is given, that is : Angle 3 = 74°
And the lines a and b are parallel, similarly line c and d are parallel to each other as well.
Now, let's just use property of angles on parallel lines to find measure of each angle we have been asked.
[tex]\qquad \tt \dashrightarrow \: \angle1 = \angle3 = 74 \degree[/tex]
[ By Corresponding Angle pair ]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle7 + \angle3 = 180 \degree[/tex]
[ By Linear Pair ]
[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - \angle3 [/tex]
[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - 74[/tex]
[tex]\qquad \tt \dashrightarrow \: \angle7 = 106 \degree[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle8 = \angle3 = 74 \degree[/tex]
[ By Vertical opposite angle pair ]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle7 = \angle11 = 106 \degree[/tex]
[ opposite angles of a Parallelogram ]
・ ．━━━━━━━†━━━━━━━━━．・
[tex]\qquad \tt \dashrightarrow \: \angle13= \angle3 = 74 \degree[/tex]
[ by Corresponding Angle pair ]