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# If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the

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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the  [#permalink]

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08 Mar 2018, 01:26
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Difficulty:

25% (medium)

Question Stats:

92% (01:49) correct 8% (01:54) wrong based on 47 sessions

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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the measure, in degrees, of angle QPS?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

Attachment:

2018-03-08_1324.png [ 18.95 KiB | Viewed 1891 times ]

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Re: If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the  [#permalink]

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08 Mar 2018, 01:27
Bunuel wrote:

If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the measure, in degrees, of angle QPS?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

Attachment:
2018-03-08_1324.png

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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the  [#permalink]

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Updated on: 08 Mar 2018, 07:16
Bunuel wrote:

If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the measure, in degrees, of angle QPS?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

Attachment:
2018-03-08_1324.png

In Triangle QRS, QR = RS & angle PRS = 100° Sum of three angle =180

Since QR = RS angle SQR = angle QSR =40

Angle PQS =180 - 40 ==> 140

As PQ = QS

Angle SPQ = Angle PSQ = 20

Hence C
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Originally posted by NandishSS on 08 Mar 2018, 01:38.
Last edited by NandishSS on 08 Mar 2018, 07:16, edited 1 time in total.
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Re: If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the  [#permalink]

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08 Mar 2018, 07:07
First, we know that QRS is 100 degrees, and that QR=RS.
Since QR=RS, the Triangle QRS is isosceles, and angle RQS = angle QSR
Triangle QRS has the angles: 100, 40, 40 (check that all angles add to 180)
Angles SQR and SQP are complementary and must add up to 180 (a straight line); if SQR=40, then SQP must=140
PQ=QS which means, just as before, Triangle PQS is isosceles, and angle SPQ = angle PSQ
Triangle PQS has the angles 140, 20, 20 (check that all angles add to 180)

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Re: If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the  [#permalink]

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12 Mar 2018, 08:48
Bunuel wrote:

If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the measure, in degrees, of angle QPS?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

Attachment:
2018-03-08_1324.png

Since QR = RS, angle QSR = angle SQR. So we can let angle QSR = n = angle SQR and create the equation:

100 + 2n = 180

2n = 80

n = 40

Thus, angle PQS = 180 - 40 = 140.

Also, since PQ = QS, angle PSQ = angle SPQ. So we can let angle angle PSQ = m = angle SPQ and create the equation:

140 + 2m = 180

2m = 40

m = 20

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Re: If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the  [#permalink]

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12 Mar 2018, 11:19
Bunuel wrote:
If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the measure, in degrees, of angle QPS?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

Attachment:

ttttt.png [ 16.93 KiB | Viewed 1287 times ]

Angles opposite equal sides are equal.

For ∆ QRS:
• two equal sides (QR = RS)
• small angles opposite those sides are equal
• ∠R = 100. Remaining interior angle degree total: (180-100) = 80°
• $$\frac{80}{2}$$ = 40° ( = ∠RQS = ∠QSR)

For ∆PQS:
• two equal sides (PQ = QS)
• small angles opposite those sides are equal
• Large ∠PQS lies on a straight line with a 40° angle
∠PQS = (180-40) = 140
• (180-140) = 40° to be split between ∠QPS and ∠PSQ

∠QPS: measure in degrees is
$$\frac{40}{2}$$ = 20° = ∠QPS

∠QPS = 20°

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Re: If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the   [#permalink] 12 Mar 2018, 11:19
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# If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the

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