Two angles of a quadrilateral measure 210° and 40°. The other two angles are in a ratio of 2:9. What are the measures of those two angles?

Angles in the ratio 2:9 are 20° and 90° respectively.

Step-by-step explanation:

Step 1: Find the 2 angles in the quadrilateral in the ratio 2:9. Let the angles be 2x and 9x.

Sum of the angles of a quadrilateral = 360°

⇒ 2x + 9x + 210° + 40° = 360°

⇒ 11x + 250° = 360°

⇒ 11x = 360 - 250 = 110°

⇒ x = 110/11 = 10

∴ Angles are 2x = 20° and 9x = 90°