Question

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

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°.

Step2: Analyze adjacent angles

∠5 and ∠6 are adjacent and form a linear - pair. So, ∠5+∠6 = 180°.

Step3: Analyze vertical - angle relationships

∠5 and ∠7 are vertical angles to a linear - pair. Since vertical angles are equal and the angles in a linear - pair are supplementary, ∠5+∠7 = 180°.
∠2, ∠3, and ∠8 do not form a linear - pair or equivalent supplementary relationship with ∠5.

Answer:

∠6 and ∠7 only