Question

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

Answer 1

Answer:

$45^{\circ}$

Step-by-step explanation:

Given:An angle is equal to one third of its supplement.

To Find:  Find its measure

Solution:

Supplementary angles : A pair of angles whose sum is 180° is called supplementary angles.

Let the angle be x

Supplement of x = 180°-x

We are given that An angle is equal to one third of its supplement.

$x=\frac{1}{3}(180-x)$

$3x=180-x$

$4x=180$

$x=45^{\circ}$

So, The angle is $45^{\circ}$

Answer 2

Answer:

45°, 135°

Step-by-step explanation:

supplementary angles:

Sum of any two angles equal to 180° is called supplementary angles.

Here,

$Let \:one \:angle = x$

$Supplementary \: angle = 180-x$

An angle is equal to one third of its supplement.(given)

$x = \frac{180-x}{3}$

$\implies 3x = 180-x$

$\implies 3x+x = 180$

$\implies 4x = 180$

$\implies x = \frac{180}{4}=45$

Therefore,

$One \:angle =x = 45\degree$

$supplementary angle = 180-45 = 135\degree$

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