Question

If two angles of a quadrilateral are ${36}^{\circ }$ and ${72}^{\circ }$ and other two angles are in the ratio 3:4, then the measure of the other two angles are

• A. ${100}^{\circ },{152}^{\circ }$
• B. ${80}^{\circ },{172}^{\circ }$
• C. ${108}^{\circ },{144}^{\circ }$
• D. ${120}^{\circ },{132}^{\circ }$

Answer 1

The correct option is C

${108}^{\circ },{144}^{\circ }$

Given the angles of a quadrilateral are 72${}^{\circ }$, 36${}^{\circ }$.

Let the other two angles be 3x and 4x
The sum of angles of a quadrilateral is ${360}^{\circ }$
$\Rightarrow 3x+4x+{36}^{\circ }+{72}^{\circ }={360}^{\circ }$
$\Rightarrow 7x={360}^{\circ }-{108}^{\circ }$
$\Rightarrow x=\frac{252}{7}={36}^{\circ }$
3x = $3\times 36={108}^{\circ }$ and 4x = $4\times 36={144}^{\circ }$
The required angles are ${108}^{\circ },{144}^{\circ }$