Question

The difference of two supplementary angles is 8 degrees. find the measure of the angles. solve using any method you like. (Be sure to define your variables).

A) x=46∘, y=134∘
B) x=50∘, y=130∘
C) x=56∘, y=124∘
D) x=62∘, y=118∘

Answer 1

The measures of two supplementary angles with a difference of 8 degrees are 86° and 94°. None of the choices provided matches these measures.

Step-by-step explanation:

The question asks us to find the measures of two supplementary angles where their difference is 8 degrees. Supplementary angles add up to 180 degrees. To solve this, let's define the variables: let x be the measure of the smaller angle, and thus the measure of the larger angle will be x + 8°. According to the property of supplementary angles, their sum is equal to 180°, which means:

x + (x + 8°) = 180°

Simplifying, we get:

2x + 8° = 180°

2x = 172°

x = 86°

Therefore, the measure of the smaller angle is 86°, and the larger angle is 86° + 8° = 94°.

None of the provided choices (A, B, C, D) match our calculation, so the correct answer is not among the listed options.