Question

An angle measures 2° less than the measure of its complementary angle. What is the measure of each angle?

Answer 1

Answer:

  angle: 44°

  complementary angle: 46°

Step-by-step explanation:

Complementary angles have a sum of 90°. We can use this relation and the one given to write equations for the angles of interest.

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setup

Let 'a' and 'c' represent the angle and its complement, respectively.

  a = c -2 . . . . . an angle is 2° less than its complement

  a +c = 90 . . . . complementary angles total 90°

solution

Using the first equation to substitute for 'a' in the second, we have ...

  (c -2) +c = 90

  2c = 92 . . . . . . add 2, collect terms

  c = 46 . . . . . . . divide by 2

  a = 46 -2 = 44 . . . . find 'a' using the first equation

The angle is 44°; its complement is 46°.