Question

find the measures of the numbered angles for each parallelogram.
39.
40.
41.

Explanation:

Step1: Use the triangle angle - sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). For the triangle with angles \(38^{\circ}\), \(110^{\circ}\), and \(\angle2\):

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Step2: Use the property of parallel lines (alternate - interior angles)

In a parallelogram, opposite sides are parallel. \(\angle1=\angle2\) (alternate - interior angles). So \(\angle1 = 32^{\circ}\)

Step3: Use the property of parallel lines (alternate - interior angles)

\(\angle3 = 38^{\circ}\) (alternate - interior angles)

Answer:

\(\angle1 = 32^{\circ}\), \(\angle2=32^{\circ}\), \(\angle3 = 38^{\circ}\)