In a quadrilateral, the ratio of the three angles is 6 : 4 : 9. The remaining fourth angle is equal to 113°. Find the difference between the largest and smallest angles of a quadrilateral.

In a quadrilateral, the ratio of the three angles is 6 : 4 : 9.

Let's assume the three angles quadrilateral are 6y, 4y, 9y.

The remaining fourth angle is equal to 113°.

The sum of all the four angles of a quadrilateral is equal to 360°.

6y + 4y + 9y + 113° = 360°

6y + 4y + 9y = 360° - 113° = 247°

19y = 247° 

y = 13°

6y = $$6\times13$$ = 78°

4y = $$4\times13$$ = 52°

9y = $$9\times13$$ = 117°

difference between the largest and smallest angles of a quadrilateral = 117°-52° = 65°