Question

parallel lines and transversals | find the... what is the measure of <1? multiple - choice question 1. understand the question 2. find angle relationships to use 3. set up the equation and solve m<3 + 110 = 180° m<3 = 70°

Explanation:

Step1: Identify angle - relationships

Since we have parallel lines and a transversal, we use the properties of angles formed by them. For example, if two angles are supplementary (sum to 180°) or corresponding, alternate - interior, etc.

Step2: Analyze given information

We know that \(m\angle3 + 110^{\circ}=180^{\circ}\) (presumably they are supplementary angles). Solving for \(m\angle3\):
\[m\angle3=180^{\circ}- 110^{\circ}=70^{\circ}\]
However, it's not clear from the provided image which angle is \(\angle1\). Assuming we use the standard angle - relationships in parallel - lines and transversal scenarios (such as corresponding, alternate - interior, alternate - exterior, or same - side interior angles), if we had more information about the position of \(\angle1\) relative to the known angles, we could find its measure. But based on the work shown in the image where \(m\angle3 = 70^{\circ}\), if \(\angle1\) and \(\angle3\) are vertical angles (opposite each other when two lines intersect), then \(m\angle1=m\angle3\).

Answer:

There is not enough information in the provided image to accurately determine the measure of \(\angle1\). If we assume \(\angle1\) and \(\angle3\) are vertical angles and \(m\angle3 = 70^{\circ}\), then \(m\angle1 = 70^{\circ}\), but this is a big assumption without clear indication of the position of \(\angle1\) in the parallel - lines and transversal setup.