Question

what reason explains why the m∠q = 115°?
a diagonals of a parallelogram bisect each other
b opposite sides of a parallelogram are congruent
c opposite angles of a parallelogram are congruent
d consecutive angles of a parallelogram are congruent
e consecutive angles of a parallelogram are supplementary

Explanation:

Step1: Recall the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary. That is, if one angle is \(x\) and its consecutive angle is \(y\), then \(x + y=180^{\circ}\).

Step2: Calculate \(m\angle Q\)

Given that one of the consecutive angles (let's assume the angle adjacent to \(\angle Q\)) is \(65^{\circ}\). Using the property of consecutive - angles in a parallelogram \(m\angle Q+65^{\circ}=180^{\circ}\). Solving for \(m\angle Q\), we get \(m\angle Q = 180^{\circ}-65^{\circ}=115^{\circ}\)

Answer:

E. consecutive angles of a parallelogram are supplementary