Question

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

• A. ${55}^{\circ },{95}^{\circ },{95}^{\circ },{115}^{\circ }$
• B. ${35}^{\circ },{115}^{\circ },{75}^{\circ },{135}^{\circ }$
• C. ${85}^{\circ },{85}^{\circ },{65}^{\circ },{125}^{\circ }$
• D. ${45}^{\circ },{75}^{\circ },{105}^{\circ },{135}^{\circ }$

Answer 1

The correct option is D ${45}^{\circ },{75}^{\circ },{105}^{\circ },{135}^{\circ }$

Ratio of four angles of a quadrilateral = 3:5:7:9
Let these angles be $3x,5x,7x$ and $9x$.

Then, $3x+5x+7x+9x={360}^0$ (Angle sum property of a quadrilateral)
$\Rightarrow 24x={360}^0\Rightarrow x=\frac{{360}^0}{24}={15}^0$

$\therefore$ First angle = $3x=3\times {15}^0={45}^0$
Second angle = $5x=5\times {15}^0={75}^0$
Third angle = $7x=7\times {15}^0={105}^0$
Fourth angle = $9x=9\times {15}^0={135}^0$