Question

Two angles are congruent and complementary. What is the measure of each angle?

A) 45°
B) 90°
C) 180°
D) The measure of each angle cannot be determined.

Answer 1

45 degrees..............

Answer 2

Answer: The correct option is (A) 45°.

Step-by-step explanation: Given that two angles are congruent and complementary.

We are to find the measure of each angle.

Since the angles are congruent, so their measures must be equal.

Let x° be the measure of each of the two angles.

We know that

the sum of the measurements of two complementary angles is 90°, so we must have

`x^\circ+x^\circ=90^\circ\\\\\Rightarrow 2x^\circ=90^\circ\\\\\Rightarrow 2x=90\\\\\Rightarrow x=(90)/(2)\\\\\Rightarrow x=45.`

Thus, the measure of each of the angles is 45°.

Option (A) is CORRECT.