Question

lines l and m are intersected by transversal t and l || m. which of the following angles are supplementary to ∠1? select all that apply. a. ∠5 b. ∠6 c. ∠7 d. ∠8

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°.

Step2: Analyze angle - relationships

Since \(l\parallel m\) and \(t\) is a transversal:

• \(\angle1\) and \(\angle5\) are corresponding angles, so \(\angle1=\angle5\), they are not supplementary.
• \(\angle1\) and \(\angle6\): \(\angle1\) and \(\angle4\) are vertical angles, \(\angle4\) and \(\angle6\) are same - side interior angles. Since \(l\parallel m\), \(\angle4+\angle6 = 180^{\circ}\), and \(\angle1=\angle4\) (vertical angles), so \(\angle1+\angle6=180^{\circ}\).
• \(\angle1\) and \(\angle7\): \(\angle1\) and \(\angle3\) are a linear pair (\(\angle1+\angle3 = 180^{\circ}\)), \(\angle3\) and \(\angle7\) are corresponding angles (\(\angle3=\angle7\)), so \(\angle1+\angle7 = 180^{\circ}\).
• \(\angle1\) and \(\angle8\): \(\angle1\) and \(\angle4\) are vertical angles, \(\angle4\) and \(\angle8\) are alternate exterior angles (\(\angle4=\angle8\)), so \(\angle1\) and \(\angle8\) are not supplementary.

Answer:

B. \(\angle6\), C. \(\angle7\)