Question

The supplement of an angel is one third of itself . Determine the angel and ite supplement

Answer 1

Answer:

Given:

The supplement of an angle is one-third of itself

To find:

The angle and its supplement

Solution:

Supplementary Angles:- When two angles add up to give 180° then they are known as supplementary pair of angles.

So,

If we assume "x°" as the angle then "(180 - x)°" is its supplement.

Also given that, the supplement of the angle is \frac{1}{3} rd

3

1

rd of itself, so we can form an equation as,

x\° = \frac{1}{3} (180 - x)\°x\°=

3

1

(180−x)\°

\implies 3x\° = (180 - x)\°⟹3x\°=(180−x)\°

\implies 3x\° + x\°= 180\°⟹3x\°+x\°=180\°

\implies 4x\° = 180\°⟹4x\°=180\°

\implies \bold{x\°= 45\°}⟹x\°=45\°

∴ Its supplement = 180 - x = 180 - 45 =\bold{135\° }180−x=180−45=135\°

Thus, the angle is 45° and its supplement is 135°.

Step-by-step explanation:

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