Two angles of a quadrilateral measure 70° and 155°. The other two angles are in a ratio of 7:20. What are the measures of those two angles?

Answer 1

Hi Owen ,

The sum of all the angles in a quadrilateral is 360 °. Since you know 2 of the angles, we can subtract those from 360° to find the "amount" left for the remaining 2 angles:

360° - 70° - 155° = 135°

The total of the remaining 2 angles will be 135°

Since the ratio of the two angles is to be set at 7:20, we can use the total of 27 and the following equivalent ratios to find the measure of one of the angles first:

7 = x

27 135

7 • 5 = x

27 5 135

x = 35°

One angle will be 35° and the other will be 100°

These two angles have a ratio of 7:20