Question

The measures of angles of a quadrilateral in degrees are $x,3x-40,2x$ and $4x+20$. Find the measure of each angle.

• A. The measures of the angles are ${55}^0,{74}^0,{62}^0$ and ${100}^0$
• B. The measures of the angles are ${28}^0,{66}^0,{102}^0$ and ${165}^0$
• C. The measures of the angles are ${38}^0,{74}^0,{76}^0$ and ${172}^0$
• D. The measures of the angles are ${50}^0,{72}^0,{80}^0$ and ${150}^0$

Answer 1

The correct option is C The measures of the angles are ${38}^0,{74}^0,{76}^0$ and ${172}^0$

Given,$x,(3x-40),2x,(4x+20)$.

We know, by angle sum property, the sum of the angles of a quadrilateral is ${360}^0$.
Therefore, $x+(3x-40)+2x+(4x+20)={360}^o$
$\Rightarrow 10x-{20}^o={360}^o$
$\Rightarrow 10x={360}^o+{20}^o={380}^o$
$\Rightarrow x=\frac{{380}^o}{10}={38}^o$.

Now, $x={38}^o$,

$2x=2\times {38}^o={76}^o$,
$3x-{40}^o=3\times {38}^o-{40}^o={74}^o$
and $4x+{20}^o=4\times {38}^o+{20}^o={172}^o$.

Thus, the measures of the angles are ${38}^o,{74}^o,{76}^o$ and ${172}^o$.

Hence, option $C$ is correct.