Question

In a right triangle, the measure of one of the acute angles is 60 degrees more than the measure of the smallest angle. Find the measures of all three angles.

Answer 1

90°, 75°, and 15°

Explanation:

In a right triangle, one of the angles is 90°.

Let x = the smallest angle

Then 60 + x = the third angle

The sum of the three angles is 180°.

90 + 60 + x + x = 180

150 + 2x = 180

2x = 30

x = 15

Measure of right angle = 90°

Measure of smallest angle = x = 15°

Measure of third angle = 60 + x = 75°

The measures of the angles are 90°, 75°, and 15°.