Question

Find the measure of an angle which is 2/3 of its suppliment

Answer 1

Step-by-step explanation:

Given :-

An angle which is 2/3 of its suppliment.

To find:-

Find the measure of the angle ?

Solution:-

Let the required angle be X°

It's supplementary angle = 180° -X°

Given that

An angle is 2/3 of its suppliment.

=> X° = (2/3)×(180°-X°)

=> 3X° = 2(180°-X°)

=> 3X° = 360°-2X°

=> 3X° +2X° = 360°

=> 5X° = 360°

=> X° = 360°/5

=> X° = 72°

Therefore , X° = 72°

Answer:-

The required angle for the given problem is 72°

Check:-

The angle = 72°

It's supplementary angle = 180°-72°=108°

2/3 of 108°

=> (2/3)×108°

=> 2×36°

=> 72°

Verified the given relations.

Used formulae:-

Supplementary Angles:-

The sum of two angles is 180° then the angles are Supplementary angles.

The supplementary angle of X° is (180-X)°

Answer 2

Answer:

ket the angle is x°

then it's supplement angle is (180-x)

so,

(180-x)2/3=x

=> 360-2x=3x

=> 360=2x+3x

=> 5x=360

=> x=360/5

=> x=72

the angle is 72°