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.

Question

asked Feb 12, 2018 73.8k views

2 Answers

Crellee · Answer 1 · 2018-02-17T13:57:27+0000

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.