Question

grade 8 mathematics

1. the diagram shows three lines with some marked angle measures.

find the missing angle measures marked with question marks.

1. the two figures are scaled copies of each other.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. For the left - hand intersection with a known angle of $70^{\circ}$, the angle opposite to it (a vertical angle) is also $70^{\circ}$.

Step2: Use linear - pair property

A linear pair of angles sums to $180^{\circ}$. So the other two angles adjacent to the $70^{\circ}$ angle are $180 - 70=110^{\circ}$ each.

Step3: Apply to right - hand intersection

For the right - hand intersection with a known angle of $53^{\circ}$, the vertical angle to it is $53^{\circ}$. And the angles adjacent to the $53^{\circ}$ angle (linear pairs) are $180 - 53 = 127^{\circ}$ each.

Answer:

For the left - hand intersection: The vertical angle to $70^{\circ}$ is $70^{\circ}$, and the other two angles are $110^{\circ}$ each. For the right - hand intersection: The vertical angle to $53^{\circ}$ is $53^{\circ}$, and the other two angles are $127^{\circ}$ each.