Question

Two angles are supplementary and the smaller is one half of the larger

Answer 1

Answer:-

Let one angle be x

Other angle = 1/2 of x => x/2

Given they are supplementary

According to the question:-

$\mathsf{x + \frac{x}{2} = 180}$

$\mathsf{ \frac{2x + x}{2} = 180}$

$\mathsf{2x + x = 180 \times 2}$

$\mathsf{3x = 360}$

$\mathsf{x = \frac{360}{3}}$

$\mathsf{x = 120}$

Therefore the other angle = 60°

Answer 2

Question : Two angles are supplementary and the smaller is one half of the larger. Find the angles .

Solution :

We know that two angles are supplementary when the sum of the two angles is 180°.

Let the measure of larger angle be x°.

Then, the measure of smaller angle = $(\frac{1}{2}\:\times\:x)^{\circ}$

= $(\frac{x}{2})^{\circ}$

Atq,

=> $x \:+\:\frac {x}{2} \:=\:180^{\circ}$

=> $\frac{2x\:+\:x}{2}\:=\:180^{\circ}$

=> $\frac{3x}{2}\:=\:180^{\circ}$

=> $3x\:=\:2\:\times\:180^{\circ}$

=> $x\:=\:\frac{360^{\circ}}{3}$

=> $x\:=\:120^{\circ}$

Measure of larger angle = 120°

Measure of smaller angle = $(\frac{120}{2})^{\circ}\:=\:60^{\circ}$

To check that our calculated angles are correct :

We know that two angles are supplementary when the sum of the two angles is 180°.

Smaller angle + larger angle = 180°

=> $60^{\circ }+120^{\circ}= 180^{\circ}$

=> $180^{\circ}= 180^{\circ}$

=>LHS = RHS