In a triangle, an exterior angle measures 145 degrees and one of the remote interior angles measures 93 degrees. What is the measure of the other remote interior angle?

In a triangle, an exterior angle measures 145 degrees and one of the remote interior angles measures 93 degrees. What is the measure of the other remote interior angle?

• A. 52 degrees
• B. 93 degrees
• C. 145 degrees
• D. 48 degrees

Answer: (A)

The exterior angle of a triangle equals the sum of the two remote interior angles. Here, 145 degrees is the exterior angle and one remote interior angle is 93 degrees. So the other remote interior angle must be 145 − 93 = 52 degrees. For a quick check, the adjacent interior angle is 180 − 145 = 35 degrees, and the three interior angles are 93, 52, and 35, which sum to 180. The measure of the other remote interior angle is 52 degrees.

The exterior angle of a triangle equals the sum of the two remote interior angles. Here, 145 degrees is the exterior angle and one remote interior angle is 93 degrees. So the other remote interior angle must be 145 − 93 = 52 degrees. For a quick check, the adjacent interior angle is 180 − 145 = 35 degrees, and the three interior angles are 93, 52, and 35, which sum to 180. The measure of the other remote interior angle is 52 degrees.