Question

The difference between two angles is ${19}^0$ and their sum is $\frac{890}{9}$ grades. Find the greater angle.
$[\text{Grade}=\frac{1}{100}$ part of rt. $\text{angle}={\left(\frac{90}{100}\right)}^0={0.9}^0]$

• A. ${63}^0$
• B. ${35}^0$
• C. ${27}^0$
• D. ${54}^0$

Answer 1

The correct option is D ${54}^0$

Let $x$ be the greater angle
Let $y$ be the smaller angle
Applying conditions, we get
$x+y=\frac{890}{9}\left({0.9}^0\right)$
$x+y={89}^0$ ...(i)
$x-y={19}^0$ ...(ii)
Adding equation (i) and (ii), we get
$2x={108}^0$
$x={54}^0$
Hence, the greater angle is ${54}^0$
Therefore, the answer is option D.