California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

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If a triangle has angles measuring 45° and 90°, what is the measure of the third angle?

30°
45°
60°
75°

The correct answer is: 45°

In any triangle, the sum of the interior angles is always 180°. Given that two angles in the triangle measure 45° and 90°, you can find the measure of the third angle by using the following calculation: First, add the two known angles: 45° + 90° = 135°. Next, subtract this sum from 180° to find the third angle: 180° - 135° = 45°. Thus, the measure of the third angle is 45°. This confirms that the correct answer is indeed that the third angle measures 45°, matching one of the triangle's existing angles. This means the triangle is an isosceles right triangle, where the two angles measuring 45° are equal, and the one measuring 90° is the right angle.