Q8: Two complementary angles have measures of a and b.​If b is 90 less than twice a, determine the measure of each angle.

Answer 1

The sum of complementary angles is 90°. For this problem, the two angles are a and b , so their sum is:

a + b = 90°

Since b is 90° less than twice a, we can substitute the following expression for b in the equation above:

2a - 90°

The equation becomes:

a + 2a - 90 = 90

Now we can solve by combing like terms and using inverse operations:

3a - 90 = 90

3a - 90 + 90 = 90 + 90

3a = 180

3a/3 = 180 /3

a = 60°

Since a and b are complementary angles, b = 30°

60°+ 30°= 90°