Answer:
m∠a = 64°
Step-by-step explanation:
The given diagram shows parallel lines A and B intersected by a transversal.
According to the Same-Side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°), so:
[tex]\sf m \angle a + 116^{\circ}=180^{\circ} \\\\ m \angle a =180^{\circ} -116^{\circ} \\\\ m \angle a =64^{\circ}[/tex]
Therefore, the measure of angle a is:
[tex]\LARGE\text{$\sf m \angle a=\boxed{\sf 64}^{\circ}$}[/tex]
