Question

Recall that two angles are complementary if the sum of their measures is 90. Find the measures of two complementary angles if one angle is 15 degree more than two times the other angle.

Answer 1

Answer: 25° and 65°

Explanation:

Let the smaller angle of the complementary angle be represented by x.

Since the other angle is 15 degree more than two times the other angle, this will be:

= (2 × x) + 15°

= 2x + 15°.

Then we add both angles together and equate them to 90° and this will be:

x + 2x + 15° = 90°

3x + 15° = 90°

3x = 90° - 15°

3x = 75°

x = 75°/3

x = 25°

Then the other angle will be:

= 2x + 15°

= (2 × 25°) + 15°

= 50° + 15°

= 65°

Therefore, the angles are 25° and 65°.