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Angle Sum Property of a Quadrilateral

The angles of...

Question

The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find the measures of these angles.

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Solution

Suppose the angles are 2x, 3x, 4x, and 6x.
We know that the sum of the angles of a quadrilateral is 360°.
∴ 2x + 3x + 4x + 6x = 360
15x = 360
x = 24

Therefore, the measures of the angles are 48°, 72°, 96° and 144°.

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