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?

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  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.

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  2. the answer can be 144 deg and 216 deg

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