Question

In a quadrilateral $ABCD$, the angles $\angle A,\angle B,\angle C$ and $\angle D$ are in the ratio $2:3:4:6$. Find the measure of each angle of the quadrilateral.

• A. ${48}^{\circ },{72}^{\circ },{96}^{\circ },{144}^{\circ }$
• B. ${38}^{\circ },{72}^{\circ },{96}^{\circ },{144}^{\circ }$
• C. ${48}^{\circ },{22}^{\circ },{96}^{\circ },{144}^{\circ }$
• D. None of these

Answer 1

The correct option is A ${48}^{\circ },{72}^{\circ },{96}^{\circ },{144}^{\circ }$

Let the angles of quadrilateral $ABCD$ are $2x,3x,4x$ and $6x$.

We know, by angle sum property, the sum of angles of quadrilateral is ${360}^o$.

$\therefore$ $\angle A+\angle B+\angle C+\angle D={360}^o$

$\Rightarrow$ $2x+3x+4x+6x={360}^o$

$\Rightarrow$ $15x={360}^o$

$\therefore$ $x={24}^o$.

$\Rightarrow$ $\angle A=2x=2\times {24}^o={48}^o$

$\Rightarrow$ $\angle B=3x=3\times {24}^o={72}^o$

$\Rightarrow$ $\angle C=4x=4\times {24}^o={96}^o$

$\Rightarrow$ $\angle D=6x=6\times {24}^o={144}^o$.

Therefore, option $A$ is correct.