Question

The average (arithmetic mean) of the measures of angle X, its complementary angle, and its supplementary angle is 80 degrees. What is the measure of the complementary of angle X? (Hint: the complementary angle of X can be represented as (90-X))

Answer 1

60°

the mean is the sum of the 3 angles divided by 3

complementary angle = 90 - x

supplementary angle = 180 - x

sum of angles = x + 90 - x + 180 - x = 270 - x

Hence

mean = $\frac{270-x}{3}$ = 80 ( multiply both sides by 3 )

270 - x = 240 ( subtract 270 from both sides )

- x = - 30 ( multiply both sides by - 1 )

x = 30

complement of x = 90 - 30 = 60°