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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
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Respuesta :

olayemiolakunle65

https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.

Therefore, the required proof and answer to the question are stated below:

a) m< TRV = 60° (given)

   m<TRS = 4x° (given)

Thus, it can be concluded from the diagram that:

<TRV ≅ m<BRW  (vertically opposite angle property)

Also,

m<TRS ≅ m<VRW (vertically opposite angle property)

But,

m<VRW = m<VRZ + m<ZRW

Thus,

m<TRV ≅ m<BRW = 60°

m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]

60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]

m<TRS + m<VRW =   [tex]360^{o}[/tex] - [tex]120^{o}[/tex]

                             = [tex]240^{o}[/tex]

2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )

m<TRS = 120

4x = 120

x = [tex]\frac{120}{4}[/tex]

  = [tex]30^{o}[/tex]

Thus, x = [tex]30^{o}[/tex]

b) The missing reason in step 3 is the angle addition postulate.

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For more clarifications on properties of vertical opposite angles, visit: https://brainly.com/question/68367

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