Question

2
multiple choice 1 point
in the figure shown,
the sum of the measures of angles 4 and
5 is 150°. what is the measure of angle 1?
105
115
30
75

Explanation:

Step1: Use the property of parallel lines and transversal

Since \(l_1\parallel l_2\), \(\angle5=\angle3\) (alternate interior angles). And \(\angle4+\angle3 = 180^{\circ}\) (linear - pair). Given \(\angle4+\angle5=150^{\circ}\), substitute \(\angle5\) with \(\angle3\), we get \(\angle4+\angle3 = 150^{\circ}\).

Step2: Find \(\angle2\)

We know that \(\angle2+\angle4+\angle3=180^{\circ}\) (straight - line angle). Since \(\angle4+\angle3 = 150^{\circ}\), then \(\angle2=180^{\circ}-(\angle4 + \angle3)=180 - 150=30^{\circ}\).

Step3: Use the property of vertical angles

\(\angle1\) and \(\angle2\) are vertical angles. So \(\angle1=\angle2\).

Answer:

\(30\)