Question

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if ( mangle rqs ) is ( 75^{circ} ), then ( mangle tpu ) is
construction for copying line ( ab )
construction of a line parallel to line ( ab ) through point ( p )
construction of a line perpendicular to line ( ab ) and line ( pu )
construction of a line perpendicular to line ( ab ) through point ( p )

Explanation:

Step1: Identify the construction type

The image shows the construction of a line parallel to line \(AB\) through point \(P\). When constructing a parallel line, we use the property of corresponding angles.

Step2: Use the property of parallel lines and corresponding angles

If two parallel lines are cut by a transversal, then corresponding angles are equal. Here, \(\angle RQS\) and \(\angle TPU\) are corresponding angles. Given \(m\angle RQS = 75^{\circ}\), so \(m\angle TPU=75^{\circ}\)

Answer:

construction of a line parallel to line \(AB\) through point \(P\); \(75^{\circ}\)