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

Angle ORP and Angle ORN are a linear pair

Explanation:

The proof will entail making use of the fact that ∠ORP and ∠ORN are supplementary. Whether their description as a linear pair is a statement or a reason will depend on your approach to the proof. Apparently, here, you are calling this fact a "statement".

The second (and subsequent) line(s) of the table might be ...

2 (statement) ORP and ORN are a linear pair. (reason) OR is a common side and R is a common vertex on line PN for these angles, hence they meet the definition of a linear pair.

3 (statement) ORP and ORN are supplementary. (reason) definition of a linear pair

4 (statement) 80 + (3x+10) = 180. (reason) substitution property; supplementary angles sum to 180 degrees

5 (statement) 3x = 90. (reason) subtraction property of equality

6 (statement) x=30. (reason) division property of equality