Question

Given: mAngleORP = 80°
mAngleORN = (3x + 10)°
Prove: x = 30

3 lines are shown. A line with points P, R, N intersects a line with points M, R, O at point O. A line extends from point R to point L between angle M R P. Angle N R O is (3 x + 10) degrees and angle P R O is 80 degrees.
Which statement could be used in step 2 when proving x = 30?

A 2-column table with 5 rows. Column 1 is labeled statements with the entries measure of angle O R P = 80 degrees semicolon measure of angle O R N = (3 x + 10) degrees, blank, blank, blank, blank. Column 2 is labeled reasons with the entries given, blank, blank, blank, blank.

AngleORP and AngleORN are a linear pair
AngleORP and AngleORN are vertical angles
80 = 3x +10
x = 30

Answer 1

Answer: "Angle ORP and Angle ORN are a linear pair."

Reason: ORP and ORN are adjacent angles that form a straight line, so they are supplementary. Then
80 + (3x + 10) = 180
3x + 90 = 180
3x = 90
x = 30.