Question

An angle measures 158° less than the measure of its supplementary angle. What is the measure of each angle? ​

Answer 1

Let's represent the measure of the first angle as x.

The measure of its supplementary angle is 180° - x.

The problem tells us that x is 158° less than the measure of its supplementary angle. So we can write:

x = (180° - x) - 158°

Simplifying this equation, we get:

2x = 22°

Dividing both sides by 2, we get:

x = 11°

So the first angle measures 11°, and its supplementary angle measures:

180° - 11° = 169°

Therefore, the measures of the two angles are 11° and 169°.

Explanation:

Answer 2

Let x be the measure of the angle in degrees.

According to the problem, the angle measures 158° less than its supplementary angle, which means the supplementary angle measures (180° - x) degrees.

Since the two angles are supplementary, their sum is 180°.

So we can write an equation:

x + (180° - x) = 180°

Simplifying and solving for x:

x + 180° - x = 180°

180° = 180°

This is always true, which means we can't solve for x using this equation.

However, we know from the first sentence that x is 158° less than its supplementary angle:

x = (180° - x) - 158°

Simplifying and solving for x:

x = 180° - x - 158°

2x = 22°

x = 11°

Therefore, the angle measures 11° and its supplementary angle measures 180° - 11° = 169°.