Question

An angle measures 64° more than the measure of its supplementary angle. What is the

measure of each angle?

Answer 1

Therefore, one angle measures 122°, and the other measures 58°.

Explanation:

Let x be the measure of one of the angles.

The supplementary angle to this angle will have a measure of 180° - x because supplementary angles add up to 180°.

According to the problem, the angle measures 64° more than its supplementary angle. So, we can write the equation:

x = (180° - x) + 64°

Now, let's solve for x:

x = 180° - x + 64°

Combine like terms:

2x = 244°

Now, divide by 2 to solve for x:

x = 244° / 2

x = 122°

So, one of the angles measures 122°, and its supplementary angle measures:

180° - 122° = 58°

Therefore, one angle measures 122°, and the other measures 58°.