The angles of a cyclic quadrilateral are in the ratio 1:2:3:4. What is the measure of the smallest angle?
36°
Let the four angles be \(x, 2x, 3x, 4x\). The sum of angles of any quadrilateral is 360°:
\(x + 2x + 3x + 4x = 10x = 360°\) \(\Rightarrow\) \(x = 36°\).
So the four angles are 36°, 72°, 108°, 144°. The smallest angle is 36°.
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