2 Answers

Quantumplation · Answer 1 · 2021-09-01T22:18:50+0000

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,

$\angle TRS + \angle TRV = 180 \degree$

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

$x + 3x = 180 \degree$

$4x = 180 \degree$

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

$x = (180 \degree)/(4)$

$x = 45 \degree$

It was given that Angle TRS is x

So, Angle TRS = 45°

Option B

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Arne De Smedt · Answer 2 · 2021-09-08T07:47:40+0000

Answer:

$\boxed {\tt B. \ x=45}$

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.

x+3x=180

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

(x+3x)=180

4x=180

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.

(4x)/(4) =(180)/(4)