Question

Two supplementary angles are in the ratio 7 : 8. Find the angles.

• A. ${94}^{\circ },{86}^{\circ }$
• B. ${74}^{\circ },{106}^{\circ }$
• C. ${80}^{\circ },{100}^{\circ }$
• D. ${84}^{\circ },{96}^{\circ }$

Answer 1

The correct option is D

${84}^{\circ },{96}^{\circ }$

Let the angles be 7x and 8x

Since the angles are supplementary , we have

$7x+8x=180°$

$15x=180°$

$x=12$

Hence the angles are 7 ( 12) = 84 ° and 8 ( 12) = 96°

Alternate Solution

Let the angles be $x^{\circ }and(180-x{)}^{\circ }$

Given

$x:(180-x)=7:8$

$\Rightarrow \frac{x}{(180-x)}=\frac{7}{8}$

$\Rightarrow 8x=7(180-x)$

$\Rightarrow 8x=7\times 180-7x$

$\Rightarrow 8x+7x=7\times 180$

$\Rightarrow 15x=7\times 180$

$\Rightarrow x=\frac{7\times 180}{15}$

$\Rightarrow x=7\times 12=84$

$\Rightarrow Theotherangle=(180-x)=180-84=96$

$\therefore Theanglesare{84}^{\circ }and{96}^{\circ }$