Question

An angle measures 39.2° less than the measure of its complementary angle. What is the measure of each angle?

Answer 1

Answer: The measures of the angles are 64.6 degrees and 25.4 degrees.

Explanation:

Complementary angles add up to 90 degrees.

x can be one angle, and (x-39.2) can be the other

x + (x-39.2) = 90

2x - 39.2 = 90

add 39.2 to both sides

2x = 129.2

divide each side by 2

x = 64.6

find the measure of the other angle

64.6-39.2 = 25.4

The measures of the angles are 64.6 degrees and 25.4 degrees.

Answer 2

25.4 and 64.6

Explanation:

Suppose two complementary angles of measures x And y then

x + y = 90 and y = x - 39.2

if we plug in x - 39.2 instead of y in the equation x + y = 90 we get :

x + (x - 39.2) = 90

then

2x = 90 + 39.2

then

2x = 129.2

then

x = 129.2/2 = 64.6

therefore

y = 64.6 - 39.2

= 25.4

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