Question

The angle of a quadrilateral are in the ratio $3:4:5:6$. The largest of them is:

• A. ${90}^{\circ }$
• B. ${120}^{\circ }$
• C. ${150}^{\circ }$
• D. ${102}^{\circ }$

Answer 1

Answer: (B)

${120}^{\circ }$

Given the ratio of angles of quadrilateral, $ABCD$ is $3:4:5:6$.

Let the angles of quadrilateral $ABCD$ be $3x,4x,5x,6x$, respectively.

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

$\Rightarrow 3x+4x+5x+6x={360}^{\circ }$

$\Rightarrow 18x={360}^{\circ }$

$\therefore x={20}^{\circ }$.

$\angle A=3x$

$=3\times {20}^{\circ }$

$={60}^{\circ }$

$\angle B=4x$

$=4\times {20}^{\circ }$

$={80}^{\circ }$

$\angle C=5x$

$=5\times {20}^{\circ }$

$={100}^{\circ }$

$\angle D=6x$

$=6\times {20}^{\circ }$

$={120}^{\circ }$

The largest angle is equal to ${120}^{\circ }.$ Hence, option $B$ is correct.