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How do you solve this question?

How do you solve this question?-example-1
User Atsuhiro Teshima
by
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1 Answer

23 votes
23 votes

Answer:

x = 8

Explanation:

We have the information that lines PQ and ST are parallel

==> m∠RPQ = m∠RTS

since they are alternate interior angles

Also because the two lines are parallel, m∠RST = m∠RPQ

Since angles ∠PRQ and ∠SRT are vertical opposite angles, they are also equal

So triangles PQR and RTS are similar triangles

Similar triangles may have different side lengths but the ratios of their side lengths are the same

In the two triangles we see that RQ = 3cm and RS= 6cm

So the ratio of each side of triangle PQR to the corresponding side is 6/3 = 2

Since side ST corresponds to side PQ, ratio of length of side ST to side PQ is also 2

This means x/4 = 2 or x = 8

User Mridul Kashatria
by
3.0k points