Question

What is the measure of an angle that is 38 degrees more than its complementary angle?

A) 38 degrees
B) 64 degrees
C) 76 degrees
D) 52 degrees

Answer 1

The measure of an angle that is 38 degrees more than its complementary angle is 64 degrees.

Step-by-step explanation:

Complementary angles are two angles whose measures add up to 90 degrees. Let's denote the measure of the unknown angle as x degrees. Since the angle is 38 degrees more than its complementary angle, we can represent the complementary angle as x - 38 degrees. Setting up the equation based on the definition of complementary angles, we have:

x + (x - 38) = 90

Simplifying this, we get:

2x - 38 = 90

Adding 38 to both sides gives us:

2x = 128

Dividing both sides by 2 gives us:

x = 64

Therefore, the measure of the unknown angle is 64 degrees.