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°.
