Question

The angle of a quadrilateral are in the ratio $2:3:4:6$. Find the measure of each of the four angles.

Answer 1

Given Ratio of angles :-$2:3:4:6$

Let each angle of the quadrilateral be $2x,3x,4x$ and $6x$.

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

$\therefore 2x+3x+4x+6x={360}^{\circ }\Rightarrow 15x={360}^{\circ }\Rightarrow x=\frac{360}{15}\Rightarrow x={24}^{\circ }$

$\therefore$ required angles are $2\times {24}^{\circ },3\times {24}^{\circ },4\times {24}^{\circ },6\times {24}^{\circ }={48}^{\circ },{72}^{\circ },{96}^{\circ },{144}^{\circ }$