A quadrilateral has two angles that measure 63° and 154°. The other two angles are in a ratio of 4:9. What are the measures of those two angles?

44° and 99°

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Subtract the 2 given angles from 360° to find the remaining sum

360° - (63 + 154)° = 360° - 217° = 143°

The 2 angles which sum to 143° are in the ratio 4 : 9

sum the parts of the ratio, 4 + 9 = 13 parts , then

143° ÷ 13 = 11° ← value of 1 part of the ratio, so

4 parts = 4 × 11° = 44°

9 parts = 9 × 11° = 99°

The other 2 angles are 44° and 99°

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