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

The reason behind the statement m∠TRS + m∠TRV = 180° is; Angle Addition Postulate

How to use angle addition postulate?

Angle addition postulate states that if D is the interior of ∠ABC, therefore, the sum of the smaller angles equals the sum of the larger angle, which from the attached image is;

m∠ABD + m∠DBC = m∠ABC.

From the attached image, we want to prove that x = 30°.

Now, T is the interior of straight angle ∠VRS.

m∠VRS = 180° (straight line angle)

Thus, from angle addition postulate, we can say that;

m∠TRS + m∠TRV = 180°.

Read more about two column proofs at;brainly.com/question/1788884

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