Question

Angles of a quadrilateral are $(4x{)}^{\circ },5(x+2{)}^{\circ },(7x-20{)}^{\circ }$ and $6(x+3{)}^{\circ }$. Find the value of $x$ (in degrees).

• A. $14$
• B. $15$
• C. $16$
• D. $18$

Answer 1

The correct option is C $16$

We know, the sum of interior angles of a quadrilateral $={360}^o$.

Given the angles are:

$4x,5(x+2),(7x-20)$ and $6(x+3).$

Then,

$4x+5(x+2)+(7x-20)+6(x+3)=360$

$\Rightarrow 4x+5x+10+7x-20+6x+18=360\Rightarrow 22x+8=360\Rightarrow 22x=360-8=352\Rightarrow x=\frac{352}{22}=\frac{176}{11}=16$

Therefore, $x=16$.

Hence, option $C$ is correct.