Question

Two angles are adjacent and form an angle of ${100}^{\circ }$. The larger is ${20}^{\circ }$ less than five times the smaller. The larger angle is

• A. ${90}^{\circ }$
• B. ${70}^{\circ }$
• C. ${80}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is C ${80}^{\circ }$

Let the smaller angle be $x$. Then,
Larger angle $=5x-{20}^{\circ }$.
Given, $x+5x-{20}^{\circ }={100}^{\circ }$
$\Rightarrow 6x={120}^{\circ }$
$\Rightarrow x={20}^{\circ }$
$\therefore$ Larger angle $=5\times {20}^{\circ }-{20}^{\circ }={80}^{\circ }$.