Question

this diagram shows three lines with some missing angle measures. complete the diagram by writing in all of the missing angle measures.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the $70^{\circ}$ angle is $70^{\circ}$. The angle vertical to the $53^{\circ}$ angle is $53^{\circ}$.

Step2: Use linear - pair property

A linear pair of angles sums to $180^{\circ}$. For the $70^{\circ}$ angle, the angle in its linear - pair is $180 - 70=110^{\circ}$. These $110^{\circ}$ angles are vertical to each other. For the $53^{\circ}$ angle, the angle in its linear - pair is $180 - 53 = 127^{\circ}$, and these $127^{\circ}$ angles are vertical to each other.

Answer:

Starting from the top - left and moving clockwise around the intersections: $110^{\circ},70^{\circ},110^{\circ},53^{\circ},127^{\circ},53^{\circ},127^{\circ}$