Question

The difference between two angles is ${19}^{\circ }$ and their sum is ${\frac{890}{9}}^o$ grades Find the greater angle

• A. ${63}^{\circ }$
• B. ${35}^{\circ }$
• C. ${27}^{\circ }$
• D. ${54}^{\circ }$

Answer 1

The correct option is D ${54}^{\circ }$

$100g={90}^0$
$\Rightarrow \frac{890}{9}g=\frac{{90}^0}{100}\times \frac{890}{9}={89}^0$
Let x and y be the given angles.
Given, $x-y={19}^0$ ...(i)
$x+y={89}^0$ ...(ii)
On adding (i) and (ii), we get
$2x={108}^0\Rightarrow x={54}^0$
from (i),$y=x-{19}^0={54}^0-{19}^0={35}^0$
Clearly, the greater angle is ${54}^0$
Option D is correct.