A quadrilateral has two angles that measure 195° and 45°. The other two angles are in a ratio of 11:13. What are the measures of those two angles?

Answer 1

The interior angles in a quadrilateral sum to 360°. We know two of the angles sum to 195° + 45° = 240°. That means the other two angles sum to 360° - 240° = 120°. Those two angles are in the part:part ratio of 11:13. The total is 11+13 = 24, so one angle is 11/24 ·120° = 55·°, the other is 13/24 ·120 = 65°.