noahmccabe1011
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Alex 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.

Line n is parallel to line m. Triangle PQR has vertex P on line n and vertices Q and R on line m. Angle QPR is 80 degrees. Segment PQ makes 40 degrees angle with line n and segment PR makes 60 degrees angle with line n.

Which is a true statement he could write?

Angle PRQ measures 40°.
Angle PQR measures 60°.
Angle PRQ measures 80°.
Angle PQR measures 40°.

Alex 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 Line n is paral class=

Respuesta :

tllawson

To prove that the sum of the measures of interior angles of triangle PQR is equal to 180°, Alex could write the following true statement:

Angle PQR measures 60°.

To see why this statement is true, we can use the fact that the sum of the measures of interior angles of a triangle is always 180°.

Let's start by finding the measure of angle PRQ. Since line n is parallel to line m, we know that angle PQM (which is opposite angle PRQ) is also 40°. Therefore, angle PRQ measures:

angle PRQ = 180° - angle PQM - angle QPR

angle PRQ = 180° - 40° - 80°

angle PRQ = 60°

Next, we can find the measure of angle PQR by using the fact that the sum of the measures of interior angles in a triangle is 180°. Since we know that angles QPR and PRQ add up to 80° + 60° = 140°, we have:

angle PQR = 180° - angle QPR - angle PRQ

angle PQR = 180° - 80° - 60°

angle PQR = 40°

Therefore, we have shown that the sum of the measures of interior angles of triangle PQR is equal to 180°, and that angle PQR measures 40°.

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