Question

which statement about the angles in the figure is true?
m∠1 + m∠8 = 90°
m∠7 + m∠10 = 180°
m∠8 + m∠9 = 90°
m∠3 + m∠5 = 180°

Explanation:

Step1: Analyze ∠3 and ∠5

∠3 and ∠5 are same - side interior angles formed by two parallel lines (implied by the triangle's structure and the transversal). By the same - side interior angles theorem, same - side interior angles are supplementary, meaning their measures add up to \(180^{\circ}\). So \(m\angle3 + m\angle5=180^{\circ}\).

Step2: Analyze other options

• For \(m\angle1 + m\angle8 = 90^{\circ}\): ∠1 and ∠8 have no such complementary relationship based on the figure's angle properties.
• For \(m\angle7 + m\angle10 = 180^{\circ}\): ∠7 and ∠10 do not form a linear pair or supplementary angles in the context of the figure.
• For \(m\angle8 + m\angle9 = 90^{\circ}\): There is no basis for ∠8 and ∠9 to be complementary.

Answer:

\(m\angle3 + m\angle5 = 180^{\circ}\)