Question

Given: mAngleTRV = 60°
mAngleTRS = (4x)°

Prove: x = 30

3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees.

What is the missing reason in step 3?

A 2-column table with 6 rows is shown. Column 1 is labeled Statements with entries measure of angle T R V = 60 degrees and measure of angle T R X = (4 x) degrees, angle T R S and angle T R V are a linear pair, measure of angle T R S + measure of angle T R V = 180, 60 + 4 x + 180, 4 x =120, x = 30. Column 2 is labeled Reasons with entries given, definition of a linear pair, question mark, substitution property of equality, subtraction property of equality, division property of equality.

substitution property of equality
angle addition postulate
subtraction property of equality
addition property of equality

Answer 1

Reason: Angles that form a linear pair are supplementary (Linear Pair Theorem / definition of supplementary angles).

So from "∠TRS and ∠TRV are a linear pair" we conclude "m∠TRS + m∠TRV = 180°."