Question

1. what is the measure of angle ( a_1 )?

Explanation:

Step1: Use the property of parallelogram

In a parallelogram \(ABCD\), \(AB\parallel CD\).

Step2: Apply the alternate - interior angles theorem

When a transversal \(AC\) intersects \(AB\) and \(CD\), \(\angle a_{1}\) and the \(40^{\circ}\) angle are alternate - interior angles.
Since alternate - interior angles are equal when two parallel lines are cut by a transversal, \(\angle a_{1}=40^{\circ}\).

Answer:

40°