The measures of two complementary angles are in the ratio of 2:6. What is the smallest angle?

(C) 22.5 degrees


Two angles are said to be complementary angles if the measure of their angles add up to 90 degrees. smaller angle + bigger angle = 90
If we let “x” be the smaller angle, then:
x + bigger angle = 90
bigger angle = 90 - x
The problem also talks about the ratio of the 2 angles. Ratio 2:6 can also be reduce and written as 1:3 for simplicity and ease of computing.

1:3 simply means that if the small angle measures x, the bigger angle measures 3x.
bigger angle = 3x
There are now two equations for the bigger angle and we can equate them.
90 – x = 3x
90 = 3x + x = 4x
4x = 90
x = 90/4 = 22.5 degrees = smaller angle

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