In a right triangle, one acute angle measures 30° more than 4 times the other. If the sum of the measures of the two acute angles must equal 90°, find the measures of the acute angles.
A) 12°, 78°
B) 14°, 76°
C) 11°, 79°
D) 13°, 82°

Question

Quizplus · Accepted Answer

Let the measure of the smaller angle be x degrees. Then, the measure of the larger angle is 4x + 30 degrees. Since the sum of the angles in a right triangle is 90 degrees (excluding the right angle), we have x + 4x + 30 = 90. Solving this equation gives x = 12 degrees for the smaller angle and 4(12) + 30 = 78 degrees for the larger angle.

In a Right Triangle, One Acute Angle Measures 30° More