Question

The larger of two supplementary angles exceeds the smaller by $24$ degrees. Then the angles are:

• A. ${112}^o,{88}^o$
• B. ${102}^o,{78}^o$
• C. ${92}^o,{68}^o$
• D. ${122}^o,{98}^o$

Answer 1

The correct option is B ${102}^o,{78}^o$

Let the two angles be $x^{\circ }$ and $y^{\circ },x>y$

According to the question,
$\Rightarrow x+y=180$ ....(1)
$\Rightarrow x=y+24$ .....(2)
Put the value of $x$ in equation (1), we get
$\Rightarrow y+(y+24)=180$

$\Rightarrow 2y=156$

$\Rightarrow y=78$

Putting this value of $y$ in equation (2), we get
$x=78+24$

$\Rightarrow x=102$
Therefore, the angles are ${102}^{\circ },{78}^{\circ }$.