Question

Two angles of a quadrilateral measure 210° and 100°. The other two angles are in a ratio of 2:3. What are the measures of those two angles?

I know the four angles add to 360 deg. So the two unknowns are 50 deg together. 20 and 30 deg angles would give a ratio of 2:3, but what is the equation I would use to figure this using the ratio and the 50 deg?

Answer 1

Larger angle = X Deg.
Smaller angle = 2X/3 Deg.
X + 2X/3 = 360 - 310 = 50,
Multiply both sides by 3:
3X + 2x = 150,
5X = 150,
X = 30 deg.
2X/3 = 2/3(30) = 20 Deg.

Answer 2

the answer can be 144 deg and 216 deg