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Virty [35]
3 years ago
13

I’m confused on this one

Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0

Remark

If the lines are parallel then triangle RQS will be similar to triangle RTP


From that, all three lines in one triangle will bear the same ratio to all three lines of the second triangle.


Givens

PQ = 8

QR = 5

RS = 15

ST = x + 3


Ratio

QR/RP = RS/RT


Sub and solve

RP = 5 + 8

RP = 13


RT = 15 + x + 3

RT = 18 + x


5/13 = 15 / (18 + x) Cross multiply

5(18 + x) = 195 Remove the brackets on the left.

90 + 5x = 195 Subtract 90 from both sides.

5x = 105 Divide by 5

x = 105/5

x = 21 Answer <<<<<<<

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Applying the linear pair theorem, the measure of angle TSV in the image given is: 86°.

<h3>How to Apply the Linear Pair Theorem?</h3>

Given the following angles in the image above:

Measure angle RSU = (17x - 3)°,

Measure angle UST = (6x – 1)°

To find the measure of angle TSV, we need to find the value of x in the given expressions as shown below:

m∠RSU + m∠UST = 180 degrees (linear pair]

Substitute the values

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m∠TSV = 180 - 2(6x - 1)

Plug in the value of x

m∠TSV = 180 - 2(6(8) - 1)

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Therefore, applying the linear pair theorem, the measure of angle TSV in the image given is: 86°.

Learn more about the linear pair theorem on:

brainly.com/question/5598970

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