Angles 1 and 2 are complementary and congruent. What is the measure of angle 1?

Solution:

Given, angles 1 and 2 are complementary and congruent.

We have to find the measure of angle 1.

Complimentary angles are the pair of angles whose sum is equal to 90 degrees.

Example: 27 degrees and 63 degrees, since 27° + 63° = 90°

Example: 60 degrees and 30 degrees, since 60° + 30° = 90°

Since angle 1 and angle 2 are complimentary, 

⇒ Angle 1 + Angle 2 = 90° ------ (1)

Also, we are given that angle 1 and angle 2 are congruent, that is, they are equal.

⇒ Angle 1 = Angle 2 ------ (2)

From (1) and (2), we have

Angle 1 + Angle 1 = 90°

⇒ 2 × Angle 1 = 90°

⇒ Angle 1 = 90°/2 = 45°

⇒ Angle 2 = 45°

Therefore, the measure of angle 1 is 45°.

Angles 1 and 2 are complementary and congruent. What is the measure of angle 1?

Summary:

Angle 1 and angle 2 are complementary and congruent. The measure of angle 1 is 45°.