Question

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

Answer 1

Given that angles in the quadrilateral are $x^{\circ },{(x+10)}^{\circ },{(x+20)}^{\circ },{(x+30)}^{\circ }$

Sum of all the angles of a quadrilateral $={360}^{\circ }$

$\therefore x^{\circ }+{(x+10)}^{\circ }+{(x+20)}^{\circ }+{(x+30)}^{\circ }={360}^{\circ }\Rightarrow 4x+{60}^{\circ }={360}^{\circ }\Rightarrow 4x={300}^{\circ }\Rightarrow x=\frac{300}{4}={75}^{\circ }$

$\therefore$ each angle is as follows

$x^{\circ }={75}^{\circ },{(x+10)}^{\circ }={85}^{\circ },{(x+20)}^{\circ }={95}^{\circ },{(x+30)}^{\circ }={105}^{\circ }$