Question

An angle is equal to one third of its supplement. Find its measure

Answer 1

given,
the angle is one third of its supplement
let the angle supplement be x
so the other angle =x/3
so x+x/3=180
L. C. M.
3x+x/3=180
4x/3=180
4x=180*3
4x=540
x=540/4
x=135

so, supplement angle is 135 degree
x/3=135/3=45 degree

Answer 2

# Solution -

Let the measure of the required angle be β.

Then, the measure of its supplement is ( 180° - β ).

It is given that -

Angle = 1/3 ( its supplement )

➟ β = 1/3 ( 180 - β )

➟ 3β = 180 - β

➟ 4β = 180°

➟ β = 180/4 = 45°

Thus, the measure of the given angle is 45°.

# Extra Information -

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

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