The angles of a quadrilateral are in the ratio $3: 4: 5: 6$. Find the measure of the angles.

Given :

The angles of a quadrilateral are in the ratio $3:4:5:6$.

To do :

We have to find the measure of the angles.

Solution :

Let the angles be 3x,4x,5x and 6x. Because $3x:4x:5x:6x = 3:4:5:6$.

We know that,

The sum of the angles in a quadrilateral is 360 degrees.

Therefore,

$3x+4x+5x+6x=360$ degrees

$18x=360$

$x= \frac{360}{18}$

$x=20°$.

The measure of the angles is $3(20)=60$ degrees, $4(20)=80$ degrees, $5(20)=100$ degrees and $6(20)=120$ dgerees.

Therefore, the measure of angles is $60°, 80°, 100°, 120°$.