Question

In a circle, two arc of unequal length subtended angles in the ratio $5:3$. If the smaller angle is ${45}^o,$ then the measure of other angle is:

• A. ${75}^o$
• B. ${72}^o$
• C. ${60}^o$
• D. ${78}^o$

Answer 1

The correct option is A ${75}^o$

Let angles be $5x$ and $3x$

Smaller angle is ${45}^o$ which is $3x$

$\Rightarrow 3x={45}^o$

$\Rightarrow x={15}^o$

$\Rightarrow 5x={75}^o$