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.
P
Linen
15°
309
135°
Line m
R
Q
(not drawn to scale)
Which is a true statement she could write? (6 points)

Options:

A) Angle PRQ measures 30°.

B) Angle PRQ measures 15°.

C) Angle PQR measures 15°.

D) Angle PQR measures 45°.

B) Angle PRQ measures 15°.

Step-by-step explanation:

Since line m is parallel to line n, Angle 30° and angle PQR are alternate interior angles. Alternate interior angles are congruent. Therefore:

The measure of angle PQR = 30°.

Also, angle 15° and angle PRQ are alternate interior angles, therefore,

The measure of angle PRQ = 15°

THUS: The sum of ∆PQR = m<PRQ + m<PQR + m<QPR

= 15° + 30° + 135° = 180°.

So, if Tamara is writing to prove that the sum of the interior angles of ∆PQR = 180°, one of the statements that she could write is that:

B) Angle PRQ measures 15°.

B:)

Step-by-step explanation:

Hope this helped

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