Question

find the measure of \\( \angle a \\) in the figure, shown to the right.
\\( m \angle a=\square \\)

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. $\angle4$ and the angle equal to $77^{\circ}$ (since the two lines are parallel and using the property of corresponding angles, $\angle2$ and $77^{\circ}$ are supplementary. But more directly, $\angle4$ and the angle which is equal to $77^{\circ}$ (by alternate - interior or corresponding angles and then vertical angles relation). In fact, when two parallel lines are cut by a transversal, the corresponding angles are equal. Then using the vertical - angle property.
We know that $\angle4$ and the angle which is equal to $77^{\circ}$ (because of parallel lines and transversal, corresponding angles and then vertical angles)

Step2: Calculate the measure of $\angle4$

Since vertical angles are equal, $m\angle4 = 77^{\circ}$

Answer:

$77$