Question

1. determine the measure of ∠1, ∠2, and ∠3 in the following diagram.

Explanation:

Step1: Find \(\angle1\)

Since \(\angle1\) and \(155^{\circ}\) are supplementary angles (they form a linear pair), we use the formula \(\angle1 + 155^{\circ}=180^{\circ}\).
So, \(\angle1=180^{\circ}- 155^{\circ}=25^{\circ}\).

Step2: Find \(\angle3\)

\(\angle3\) and \(155^{\circ}\) are vertical angles. Vertical angles are equal.
So, \(\angle3 = 25^{\circ}\) (because \(\angle1\) and \(\angle3\) are also vertical angles, and we know \(\angle1 = 25^{\circ}\)).

Step3: Find \(\angle2\)

\(\angle2\) and \(\angle3\) are vertical angles.
So, \(\angle2=155^{\circ}\) (because \(\angle2\) and \(155^{\circ}\) are vertical angles).

Answer:

\(\angle1 = 25^{\circ}\), \(\angle2=155^{\circ}\), \(\angle3 = 25^{\circ}\)