Question

problem 1
here are three intersecting lines.
determine the missing angle measurements.
45°
80°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle opposite the $45^{\circ}$ angle has a measure of $45^{\circ}$.

Step2: Use linear - pair property

A linear pair of angles sums to $180^{\circ}$. The angle adjacent to the $80^{\circ}$ angle on a straight - line has a measure of $180 - 80=100^{\circ}$.

Step3: Use angle - sum property in a triangle - like formation

Let's consider the intersection of the three lines. We know one angle is $45^{\circ}$ and another is $80^{\circ}$. The third angle (the remaining unknown angle) in the non - triangle formed by the intersection of the lines can be found using the fact that the sum of angles around a point is $360^{\circ}$ or by considering the angles on a straight - line and angle relationships. The third unknown angle adjacent to the $45^{\circ}$ and $80^{\circ}$ angles (in the relevant part of the intersection) is $180-(45 + 80)=55^{\circ}$.

Answer:

The missing angles are $45^{\circ}$, $100^{\circ}$, $55^{\circ}$ (in the order corresponding to the problem's layout from top - right, bottom - left, and the other non - given angle respectively)