Question

An angle is equal to five times its complement. Determine the angle.

Answer 1

Answer is 36•

Let the angle be x

A.T.Q

5x=180•

x=36•

Answer 2

# Solution -

Let the measure of the given angle be β.

Then, the measure of its complement is ( 90° - β ).

It is given that -

Angle = 5 × Its complement

➟ β = 5 ( 90° - β )

➟ β = 450° - 5β

➟ 6β = 450°

➟ β = 450°/6 = 75° ______[ANSWER]

Thus, the measure of the given angle is 75°.

# Extra Information -

Two angles, the sum of whose measure is 180°, are called supplementary angles.

(αttαchєd fígurє 1)

Two angles, the sum of whose measure s is 90°, are called complementary angles.

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Thus, Angle BAX and Angle XAC are complementary angles, if x + y = 90°