Question

In a quadrilateral the angles are in the ratio $3:4:5:6$. Then the difference between the greatest and the smallest angle is?

• A. ${108}^o$
• B. ${60}^o$
• C. ${80}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${60}^o$

Given 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 ${360}^o$.

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

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

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

$\therefore \angle A=3x=3\times {20}^o={60}^o$,

$\angle B=4x=4\times {20}^o={80}^o$,

$\angle C=5x=5\times {20}^o={100}^o$

and $\angle D=6x=6\times {20}^o={120}^o$.

$\therefore$ The greatest angle is $={120}^o$

and the smallest angle is $={60}^o$.

Therefore, the difference between the greatest and the smallest angle is $={120}^o-{60}^o={60}^o$.

Hence, option $B$ is correct.