The two angles of a quadrilateral are 76° and 68°. If the other two angles are in the ratio of 5 : 7, then find the measure of each of them.

Question: The two angles of a quadrilateral are 76° and 68°. If the other two angles are in the ratio of 5 : 7, then find the measure of each of them.

Solution:
Given two angles are 76° and 68°.
Let the other two angles be 5x and 7x.
As we know, the sum of interior angles of a quadrilateral is 360°.

Therefore,
76° + 68° + 5x + 7x = 360°
⇒ 144° + 12x = 360°
⇒ 12x = 360° - 144°
⇒ 12x = 216°
⇒ x = 216°/12
∴ x = 18°

Hence, the other two angles are:
5x = 5(18)° = 90°
7x = 7(18°) = 126°.