The measure of an angle is four times the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Let the measure of the angle be x degrees.

Since the angle is four times the measure of its supplementary angle, we can write:

x = 4(180 - x)

Expanding the right side, we get:

x = 720 - 4x

Adding 4x to both sides, we get:

5x = 720

Dividing both sides by 5, we get:

x = 144

So, the measure of the angle is 144 degrees, and the measure of its supplementary angle is 180 - 144 = 36 degrees.

Answer 2

An angle measures 84° less than the measure of its complementary angle. What is the measure of each angle?

Answer 3

Let's denote the measure of the angle as x degrees.

The complementary angle to the angle is 90° - x because the sum of a complementary angle pair is 90 degrees.

According to the given information, the angle measures 84° less than its complementary angle:

x = (90 - x) - 84

Simplifying this equation, we get:

x = 90 - x - 84
x = 6 - x
2x = 6
x = 3

Therefore, the angle measures 3 degrees, and its complementary angle measures 90 - 3 = 87 degrees.