Question

An angle measures 164° less than the measure of its supplementary angle. What is the measure of each angle?

A) 148° and 28°
B) 82° and 98°
C) 82° and 246°
D) 82° and 164°

Answer 1

The measure of the smaller angle is 82°, and the measure of its supplementary angle is 98°. OPTION B

Step-by-step explanation:

Let's denote the measure of the smaller angle as 'x'. According to the given information, the larger (supplementary) angle measures 164° more than the smaller angle. Therefore, the measure of the larger angle is x + 164°.

Since the angles are supplementary, their sum is 180°. So, we can set up the equation:

x + (x + 164) = 180

Combine like terms:

2x + 164 = 180

Subtract 164 from both sides:

2x = 16

Divide by 2:

x = 8

So, the measure of the smaller angle is 8°. To find the larger angle, add 164:

x + 164 = 8 + 164 = 172

Therefore, the measure of the larger (supplementary) angle is 172°. The pair of angles that satisfies these conditions is represented by option B) 82° and 98°.