Question

The difference of two complementary angles is 55 degrees. Find the measures of the angles.

Answer 1

The tow angles are 17.5 o and 72.5 o Solution Complementary angles add up to 90

Answer 2

α = 72.5°

β = 17.5°

Explanation:

Let's call the two angles α and β.

Complementary angles are those that add up to 90 degrees.

α + β = 90° [1]

The difference of two complementary angles is 55 degrees.

α - β = 55° [2]

Let's add [1] and [2] side to side.

α + β + α - β = 90° + 55°

2α = 145°

α = 72.5°

From [1],

α + β = 90°

72.5°C + β = 90°

β = 17.5°