Question

problem 5
this diagram shows three lines with some missing angle measures.
complete the diagram by writing in all of the missing angle measures.
70°
53°

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 the linear - pair is $180 - 70=110^{\circ}$. And the other angle in the linear - pair with this $110^{\circ}$ angle is also $70^{\circ}$ (vertical angles). For the $53^{\circ}$ angle, the angle in the linear - pair is $180 - 53 = 127^{\circ}$, and the other angle in the linear - pair with this $127^{\circ}$ angle is $53^{\circ}$ (vertical angles).

Step3: Consider intersection of lines

At the intersection of the three lines, we can find all the angles. The angles around the intersection points are either vertical angles or in a linear - pair.

Answer:

The missing angles (clock - wise starting from the top - left intersection near the $70^{\circ}$ angle): $110^{\circ},70^{\circ},110^{\circ}$; at the other intersection (clock - wise starting from the top near the $53^{\circ}$ angle): $127^{\circ},53^{\circ},127^{\circ}$