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

The angles are 23° , 67°.
Step-by-step 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°.