Use the triangle sum conjecture to determine each lettered angle measure.

Pls help!

Answer:

a = 69

b = 47

c = 116

d = 93

e = 86

See ALL MATH below!

Step-by-step explanation: (PLEASE READ!!!) ;3

remember that the sum of all the angles in a triangle will always add up to be 180.

All angles in a quadrilateral will be 360.

Pentagon, 540, and the center shape in your problem, hexagon, 720°

It's easier to think about this problem when you look at the two separate triangles, and not the small individual shapes. SO...

one of them, the one that points down, only has a single missing angle (a)

we can find that by doing this:

40 + 71 = 111

180 - 111 = 69

so a = 69

to find B, it's actually more simple. b+133, the angle next to it, will add up to 180, because it's a straight line. so...

180-133 = 47, so B = 47

now that you have a and b,  we can find c by using the same method we used to find b, but first we need the angle next to it, so we use the method to find a!

180 - (a + b) = needed angle

180 - needed angle = c

69 + 47 = 116

180-116 = 64

now we have 64. we will subtract that from 180 to get c!

180- 64 = 116

the easiest way to find d is to find the other angle in that small triangle to the bottom right, so we'll subtract 140 from 180, which is 40. 47 + 40 = 87

180 - 87 = 93

d = 93!

finally for e, I'm going to do my work below, I'll have to find many other angles to get e, so maaaaybe you'll be able to follow along.

71+40=111, 180 - 111 = 69

180 - 69 = 111

111 is the angle to the left of the given 140.

NOW we can focus on that little triangle to the left, after we get the bottom left most angle, we can add that with 47, subtract it from 180, and we'll have e!!!

180-111 = 69   (bottom right angle of little triangle)

180-116 (c) = 64 (top angle)

69 + 64 = 133

180 - 133 = 47!!

Now we have two angles of the large triangle that points up. using them, we can find the last one, E.

47 + 47 = 94

180 - 94 = e

WhiCH IS....

DRUMROLL...

86!

:D

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