Question

The angles of quadrilateral are in the ratio $2:1:5:4$. what is the difference between smallest and the largest angle of the quadrilateral?

• A. ${120}^o$
• B. ${130}^o$
• C. ${110}^o$
• D. ${30}^o$

Answer 1

The correct option is A ${120}^o$

Let the angles be $2x,x,5x$ and $4x$
also, $\text{sum of all interior angles of quadrilateral}={360}^o$
$2x+x+5x+4x={360}^o$
$12x={360}^o$
$x=\frac{{360}^o}{12}$
$x={30}^o$

So smallest angle is $x$ which is ${30}^o$
And largest number is $5x$ which is $5\times {30}^o={150}^o$
$\text{Difference between smallest and largest number}={150}^o-{30}^o$
$={120}^o$

Hence, correct answer is option $\left(a\right)$.