The angles (x-24)° and 3x° are supplementary angles, so their sum is 180°.
x - 24 + 3x = 180
4x - 24 = 180
4x = 204
x = 51
m∠A = 3x = 3 * 51 = 153°
Since 153° is not an option, angle A and 3x are congruent corresponding angles, meaning they are equal. m∠A = 3x.
The given angle (x-24) and m∠A are a linear pair and add to 180.
x - 24 + 3x = 180
4x = 204
x = 51
m∠A = 3 * 51 = 153
Since ∠A is not a given answer, we'll look at the consecutive interior angle that is supplementary to ∠A.
180 - 153 = 27 degrees. 27 is not a choice.
If 3x = m∠A and the other given angle is x - 24, these form a linear pair and must add up to 180.
3x + x - 24 = 180
4x = 204
x = 51
If x - 24 is 51 - 24 = 27, then m∠A can be found using supplementary angles which add to 180.
180 - 27 = 153, which isn't an answer.
The correct answer must be 27 degrees by looking at the choices available and by finding the supplementary angle to the 3x.
However, the problem is set up strangely. Assuming 3x = m∠A is not correct in this diagram.
The question states "find m∠A", and so based on solving it, 3x = 3(51) = 153.
Angle A is supplementary with the angle x - 24 = 51 - 24 = 27. 180 - 27 = 153.
The angles (10x - 27)° and 7x° are consecutive interior angles, so their sum is 180°.
10x - 27 + 7x = 180
17x - 27 = 180
17x = 207
x = 12.18. This gives an angle measure of 7(12.18) = 85.23
m∠B = 7x = 7 * (12.18) ≈ 85
m∠B must be one of the answer choices.
The angles are formed by parallel lines and a transversal.
The two given angles are consecutive interior angles, so they are supplementary.
10x - 27 + 7x = 180
17x = 207
x ≈ 12.18
7x ≈ 85.26
10x - 27 ≈ 94.76
The two should add up to 180. 85.26 + 94.76 ≈ 180.
Since m∠B = 7x, B must equal 85 degrees to be closest.
However, 71 is the closest answer and is probably meant to be the correct choice.
The angles (5x - 1)° and (6x - 13)° are vertical angles, therefore they have equal measure.
5x - 1 = 6x - 13
-1 + 13 = 6x - 5x
12 = x
m∠C = 5x - 1 = 5 * 12 - 1 = 60 - 1 = 59°. The closest answer is 56.
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