Question

The sum of the measures of two complementary angles

is 90°. If one angle measures 21° more than 2 times
the measure of its complement, find the measures of
the two angles.
The smaller angle x measures

Answer 1

The angles are 23° , 67°.

Explanation:

Complementary angles:

If sum of two angles is 90°, then they are called complementary angles.

Let one angle be 'x'.

Its complement = 2*x + 21 = 2x + 21

x + 2x + 21 = 90°

3x + 21 = 90

Subtract 21 from both sides,

3x = 90 - 21

3x = 69

Divide both sides by 3,

x = 69/3

x = 23°

Its complement = 2*23 + 21

= 46 + 21

= 67°

Two complementary angles are 67° and 23°.