Two parallel lines are cut by a transversal. The co-interior angles are in the ratio 1 : 3. Find the smaller angle.
45°
Co-interior (allied) angles formed by a transversal on parallel lines are supplementary, so their sum is 180°.
Let the angles be \(x\) and \(3x\). Then \(x + 3x = 180^\circ \Rightarrow 4x = 180^\circ \Rightarrow x = 45^\circ\).
The smaller angle is 45°.
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