Question

1. use the diagram below to find ( mangle2 ).

( 30^{circ})
( 70^{circ})
( 110^{circ})
( 180^{circ})

Explanation:

Step1: Find the measure of ∠1

Since the angle of \(110^{\circ}\) and ∠1 are supplementary (they form a linear pair), we use the formula \(∠1 + 110^{\circ}=180^{\circ}\).
So, \(∠1=180^{\circ}- 110^{\circ}=70^{\circ}\).

Step2: Use the property of parallelogram

The figure is a parallelogram (opposite sides are parallel). In a parallelogram, opposite angles are equal. But here, we can also use the property that consecutive angles in a parallelogram are supplementary. However, another approach: since \(WZ\parallel XY\) and \(WY\) is a transversal, and \(WX\parallel ZY\), we can also note that \(∠2 = ∠1\) (alternate - interior angles for parallel lines \(WX\parallel ZY\) and transversal \(WY\)).

Answer:

\(70^{\circ}\)