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

This is known to be the law that state that when one put two or more angles side by side making them to share a common vertex and also an arm between the both pair of angles, then the sum of those angles will then be the same with the total sum of the resulting angle.

Since T = is the interior of straight angle ∠VRS.

m∠VRS = 180° ( is a straight line angle)

So, based on the angle addition postulate says that:

m∠TRS + m∠TRV = 180°.

Therefore, since the proof for x = 30, the missing reason in step 3 is angle addition postulate.

Learn more about angle addition postulate from

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