Question

If two angles of a quadrilateral are ${36}^{\circ }$ and ${72}^{\circ }$ and the other two angles are in the ratio 2:4, then the measure of the other two angles are _____.

• A. ${84}^{\circ },{168}^{\circ }$
• B. ${76}^{\circ },{160}^{\circ }$
• C. ${108}^{\circ },{144}^{\circ }$
• D. ${72}^{\circ },{108}^{\circ }$

Answer 1

The correct option is A ${84}^{\circ },{168}^{\circ }$

Let two angles be 2x and 4x
The sum of angles of a quadrilateral is ${360}^{\circ }.$
$2x+4x+{36}^{\circ }+{72}^{\circ }={360}^{\circ }$
$6x={360}^{\circ }-{108}^{\circ }$
$x=\frac{252}{6}={42}^{\circ }$
Hence, the other two angles are,
$2x=2\times 42={84}^{\circ }$
$4x=4\times 42={168}^{\circ }$
The required angles are
${84}^{\circ },{168}^{\circ }.$