Question

The measures of the consecutive angles of a quadrilateral are in the ratio$5:7:11:13$ . Find the measure of each angle.

Short answer

The measure of each angle is${50}^{\circ },{70}^{\circ },{110}^{\circ }$ and${130}^{\circ }$ .

Step-by-step solution

Step 1. Given information.

The ratio of the consecutive angles of a quadrilateral are,

$5:7:11:13$

Step 2. Concept used.

The sum of angles of a quadrilateral is${360}^{\circ }$

Since, ratio of the angles is always in the simplified form,

it might not represent the actual measure.

So,

Step 3. Considering the angles as5x,7x,11x,13x. 

The sum of the angles of the quadrilateral can be expressed using the above relation as,

$\begin{array}{c}5x+7x+11x+13x=360\\ 36x=360\\ x=10\end{array}$

So each of the angles are given by,

$\begin{array}{c}5x=5\times 10\\ =50\\ 7x=7\times 10\\ =70\\ 11x=11\times 10\\ =110\\ 13x=13\times 10\\ =130\end{array}$

Therefore, the measure of each angle of quadrilateral is${50}^{\circ },{70}^{\circ },{110}^{\circ }$ and${130}^{\circ }$ .