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Sarah06109

Answer:

[tex]\boxed {\tt B. \ x=45}[/tex]

Step-by-step explanation:

x and 3x are on a straight line together. Therefore, they are supplementary and must add to 180 degrees.

Add x and 3x, and set that equal to 180.

[tex]x+3x=180[/tex]

Combine like terms on the right side of the equation. Both x and 3x have a variable, so they can be added together.

[tex](x+3x)=180[/tex]

[tex]4x=180[/tex]

Since we want to find x, we have to isolate x. x is being multiplied by 4. The inverse of multiplication is division. Divide both sides of the equation by 4.

[tex]\frac{4x}{4} =\frac{180}{4}[/tex]

[tex]x=\frac{180}{4}[/tex]

[tex]x=45[/tex]

x is equal to 45, so the correct answer is B. 45

FadedElla

In the diagram, we can see that two lines are intersecting and a two pairs of vertically opposite angles are forming. The angle on a line are supplementary to each other (linear pair).

  • Supplementary angles add upto 180°.

Here, angle TRS and angle TRV are linear pair, so they will have a sum of 180°.

Then,

[tex] \angle TRS + \angle TRV = 180 \degree[/tex]

In the question, given angle TRS = x and angle TRV = 3x

[tex]x + 3x = 180 \degree[/tex]

[tex]4x = 180 \degree[/tex]

Now, divide 4 from both sides because we need to find x.

[tex]x = \frac{180 \degree}{4} [/tex]

[tex]x = 45 \degree[/tex]

It was given that Angle TRS is x

So, Angle TRS = 45°

Option B

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