Question

In a quadrilateral, the angles are $x^{\circ },(x+10{)}^{\circ },(x+20{)}^{\circ },(x+30{)}^{\circ }$. Find the value of $x$.

• A. ${175}^{\circ }$
• B. ${275}^{\circ }$
• C. ${375}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is D ${75}^{\circ }$

The given quadrilateral angles are $x^o,(x+10{)}^o,(x+20{)}^o$ and $(x+30{)}^o$.

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

$\therefore$ $x^o+(x+10{)}^o+(x+20{)}^o+(x+30{)}^o={360}^o$

$\Rightarrow$ $4x^o+{60}^o={360}^o$

$\Rightarrow$ $4x^o={300}^o$

$\Rightarrow$ $x^o={75}^o$.

$\therefore$ The value of $x$ is ${75}^o$.

Hence, option $D$ is correct.