Question

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

Answer 1

Angles are in the ratio$=2:3:4:6$

Let's assume the angles to be $2x,3x,4x$ and $6x$

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

$\Rightarrow 2x+3x-4x+6x={360}^o$

$\Rightarrow 15x={360}^o$

$\Rightarrow x={360}^o/15={24}^o$

Hence, the angles are as follows:

$2x=2\times {24}^o={48}^o$

$3x=3\times {24}^o={72}^o$

$4x=4\times {24}^o={96}^o$

and $6x=6\times {24}^o={144}^o$.