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505-555 (Easy)|   Geometry|      
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Bunuel
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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the 08 Mar 2018, 02:26
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C
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15% (low)

Question Stats:

92% (01:41) correct 8% (01:51) wrong based on 60 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

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2018-03-08_1324.png
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C
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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the 08 Mar 2018, 02:27
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Bunuel

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

Show Spoiler
Attachment:
2018-03-08_1324.png
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23. Geometry




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29. Graphs and Illustrations



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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the Updated on: 08 Mar 2018, 08:16
Originally posted by NandishSS on 08 Mar 2018, 02:38.
Last edited by NandishSS on 08 Mar 2018, 08:16, edited 1 time in total.
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Bunuel

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

Show Spoiler
Attachment:
2018-03-08_1324.png
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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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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the 08 Mar 2018, 08:07
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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)

The answer is C
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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the 12 Mar 2018, 09:48
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Bunuel

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

Show Spoiler
Attachment:
2018-03-08_1324.png
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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

Answer: C
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If PQ = QS, QR = RS and the measure of angle PRS = 100°, what is the 12 Mar 2018, 12:19
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Bunuel

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
Show more
Attachment:
ttttt.png
ttttt.png [ 16.93 KiB | Viewed 13289 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°

Answer C
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