Question

tamara 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.
(image of triangle pqr with lines m and n, angles at p: 30°, 135°, 15°; lines m and n are parallel)
( not drawn to scale)
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

Since line \(n \parallel m\), the \(15^\circ\) angle at \(P\) is alternate interior to \(\angle PRQ\).

Step2: Conclude angle measure

By alternate interior angles theorem, \(\angle PRQ = 15^\circ\).

Step3: Verify other options

• \(\angle PQR\) is alternate interior to \(30^\circ\), so \(\angle PQR=30^\circ\), eliminating other choices.

Answer:

Angle PRQ measures 15°