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Aleonysh [2.5K]
3 years ago
13

2. Two angles are supplements if their sum is 180 degrees. The measure of one angle is seven-fifths the measure of its supplemen

t. What is the measure of the smaller angle?
Mathematics
2 answers:
dusya [7]3 years ago
8 0
The answer is fiftycfour degrees have fun lol
dybincka [34]3 years ago
8 0
X = 7/5(180 - x)
x = 1260/5 - 7/5x
7/5x + x = 252
7/5x + 5/5x = 252
12/5x = 252
x = 252 / (12/5)
x = 252 * 5/12
x = 1260/12
x = 105

180 - x =
180 - 105 =
75

so the smaller angle is 75
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Sorry, it's late, and I'm a bad explainer.

The error is adding (2x-12) with x and 30. This is wrong because you are adding the angles inside the triangle and you are assuming that (2x - 12) is the unlabeled angle INSIDE the triangle, when it is the exterior angle/outside of the triangle.

A straight line is also 180°.

(2x - 12) + ? = 180

30 + x + ? = 180

If you look at the equations, and put parentheses around 30 + x, (30 + x) and (2x - 12) should be the SAME NUMBER. So you could set them equal to each other to find x. (or you could also look at the picture and see that they both need/are missing the same angle)

2x - 12 = 30 + x

x = 42

Now you plug 42 into the exterior angle equation

2(42) - 12 = 84 - 12 = 72°

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