Question

The difference between two angles is ${19}^{\circ }$ and their sum is $\frac{890}{9}$ grades . Find the greater angles.
$[Grade=\frac{1}{100}partofrtangle={\left(\frac{90}{100}\right)}^{\circ }={0.9}^{\circ }]$

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

Answer 1

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

1 Grade = $\frac{1}{100}$ of right angle
$=\left({\frac{90}{100}}^{\circ }\right)={0.9}^{\circ }degree$
Let the two angles be $\alpha and\beta$
$\therefore \alpha +\beta =\frac{890}{9}grade=\frac{890}{9}\times \frac{9}{10}={89}^{\circ }$
and $\alpha -\beta ={19}^{\circ }$
$\therefore 2\alpha =89+19={108}^{\circ }$
therefore Greater angle $\alpha =\frac{1}{2}\left({108}^{\circ }\right)={54}^{\circ }$