Question

The angles of a quadrilateral are in the ratio $3:5:7:9$. Find the measure of the greatest angle.

• A. ${75}^{\circ }$
• B. ${85}^{\circ }$
• C. ${105}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

The correct option is D ${135}^{\circ }$

Let four angles be $3x,5x,7x$ and $9x$.
The sum of angles of a quadrilateral is ${360}^{\circ }$.
Therefore,
$3x+5x+7x+9x={360}^{\circ }$
$\Rightarrow 24x={360}^{\circ }$
$\Rightarrow x={15}^{\circ }$
So,
Greatest angle $9x=9\times {15}^{\circ }$
$={135}^{\circ }$