Charlotte 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 description: 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 70 degrees. Segment PQ makes 35 degree angle with line n and segment PR makes 75 degree angle with line n.

Which is a true statement she could write?

Options:
A. Angle PRQ measures 35°.
B. Angle PRQ measures 75°.
C. Angle PQR measures 70°.
D. Angle PRQ measures 70°.

See image attached for visual.

Angle PRQ measures 75 degrees.

Explanation:

Angle Q = 35 degrees

   The angle opposite is equal because both lines are parallel.

Since a triangle must equal 180 degrees, one can solve angle PQR by adding the two angles together and subtracting that from 180.

   35 + 70 = 105

   180 - 105 = 75

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B. Angle PRQ measures 75°.

Step-by-step explanation:

step-by-step explanation:

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for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c