Question

The angles of a quadrilateral are in ratio $4:5:7:8$. Find the measure of each angle.

Answer 1

We have a quadrilateral whose angles are given in the ratio $4:5:7:8$

So, its angles are $4x,5x,7x,8x$ ( where x is some constant )

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

$$\begin{gathered} \Rightarrow 4x+5x+7x+8x=360° \\ \Rightarrow 24x=360° \\ \Rightarrow x=\frac{360°}{24} \\ \Rightarrow x=15 \end{gathered}$$

So, angles are;

$$\begin{gathered} 4\times 15=60° \\ 5\times 15=75° \\ 7\times 15=105° \\ 8\times 15=120° \end{gathered}$$

So, the required angles are ${60}^{\circ },{75}^{\circ },{105}^{\circ },{120}^{\circ }$