Question

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 other two angles are

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

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