Question

which of the angles in the figure are supplementary to ∠5? m n ∠6 only ∠6 and ∠7 only ∠8 only ∠2,∠3,∠6 and ∠7

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°.

Step2: Analyze adjacent angles

∠5 and ∠6 are adjacent angles on a straight - line formed by line n and the transversal. So, ∠5+∠6 = 180°.

Step3: Analyze vertical - angle relationship

∠5 and ∠7 are vertical angles to a pair of supplementary angles. Since vertical angles are equal, and if we consider the supplementary pair related to ∠7, ∠5+∠7 = 180°.

Step4: Check other angles

∠5 and ∠8 are vertical angles, so ∠5=∠8, and they are not supplementary. Also, ∠5 has no direct supplementary relationship with ∠2 and ∠3.

Answer:

∠6 and ∠7 only