Question

question 3
tanara is writing statements to prove that the sum of the measures of interior angles of triangle pqr is equal to 180°. line m is parallel to line n
which is a true statement she could write?
angle prq measures 30°
angle prq measures 15°
angle pqr measures 15°
angle pqr measures 45°

Explanation:

Step1: Use alternate interior angles property

When two parallel lines are cut by a transversal, alternate interior angles are equal. Line \(m\) is parallel to line \(n\). The angle of \(30^{\circ}\) (on line \(n\)) and \(\angle PRQ\) are alternate - interior angles.

Step2: Check each option

• For the option “Angle \(PRQ\) measures \(30^{\circ}\)”:

Since line \(m\parallel n\) and they are cut by the transversal \(PQ\) (for the \(30^{\circ}\) angle part), by the alternate - interior angles theorem, \(\angle PRQ = 30^{\circ}\).

• For the option “Angle \(PRQ\) measures \(15^{\circ}\)”:

This is incorrect as per the alternate - interior angles property.

• For the option “Angle \(PQR\) measures \(15^{\circ}\)”:

There is no information (using parallel - line properties like alternate interior, corresponding or same - side interior angles) to support this.

• For the option “Angle \(PQR\) measures \(45^{\circ}\)”:

There is no information (using parallel - line properties like alternate interior, corresponding or same - side interior angles) to support this.

Answer:

Angle \(PRQ\) measures \(30^{\circ}\)