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SVEN [57.7K]
3 years ago
6

4. Find x if PQ = RS, PQ = 9x - 7, and RS = 29.

Mathematics
1 answer:
Gnoma [55]3 years ago
4 0

Answer:

x=4

Step-by-step explanation:

Because we know that PQ = RS, we can use the transitive property to replace PQ in the first equation with 29:

9x-7=29

1) Add 7 to both sides:

9x=36

2) divide by 9 on both sides:

x=4

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<h3><u>Finding the measure of all other angles with proof:</u></h3>

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<u>∠3:</u>

∠1  = ∠3            <em>(Angle 1 and 3 are vertically opposite)</em>

65 = ∠3             <em>(Angle 1 = 65°)</em>

<em>∠3 = 65°</em>

<em />

<u><em>∠4:</em></u>

∠4 = ∠2                  <em>(Vertically opposite angles)</em>

∠4 = 115°                <em>(∠2 = 115°)</em>

<u><em /></u>

<u>∠5:</u>

∠5 = ∠1          <em>(Corresponding angles)</em>

∠5 = 65°        <em>(∠1 = 65°)</em>

<u><em /></u>

<u>∠6:</u>

∠6 = ∠2      <em>(Corresponding angles)</em>

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<em />

<u>∠7:</u>

∠7 = ∠3        <em>(Corresponding Angles)</em>

∠7 = 65°       <em>(∠3 = 65°)</em>

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∠8 = ∠4        <em>(Corresponding angles)</em>

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The complete proof for the given parallelogram is given in the image attached below.

<h3>What is a Parallelogram?</h3>

A parallelogram is a quadrilateral whose opposite sides are parallel and also congruent to each other.

The complete proof would be as shown below:

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Learn more about parallelogram on:

brainly.com/question/3050890

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