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sritamasia
Updated on: 28 Nov 2021, 03:07
Originally posted by sritamasia on 27 Nov 2021, 15:49.
Last edited by Bunuel on 28 Nov 2021, 03:07, edited 3 times in total.
Last edited by Bunuel on 28 Nov 2021, 03:07, edited 3 times in total.
Renamed the topic and edited the question.
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Difficulty:
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63% (01:51) correct
38%
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based on 48
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In the figure below, find \(\angle QPR\)?
(1) \(AB || CD\)
(2) \(\angle CRP = \angle PRQ\) and \(\angle AQP = \angle PQR\)
Attachment:
trian.jpg [ 6.82 KiB | Viewed 1550 times ]
28 Nov 2021, 02:48
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We need to find the exact value for angle QPR = ?
S1: just knowing that 2 lines are parallel doesn’t help us get exact values. The triangle formed by QPR could move around in all kinds of directions.
Not sufficient
S2: we are not given any values - it’s not possible to find a unique value
Together
Since AB and CD are parallel, line QR becomes a Transversal line intersecting the 2 parallel lines
This gives us certain unique relationships among the angles. One of those is that the “same side” interior angles are Supplementary, or they SUM to 180 degrees.
This means:
Angle <AQR + Angle < CRQ = 180 degrees
We are told that the 2 angles at point R are equal —- call each angle X so that the entire Angle <CRQ = 2X
We are also told that the 2 angles at point Q are equal —— call each angle Z so that the entire Angle <AQR = 2Z
Substitute into the equation above
2Z + 2X = 180
Z + X = 90
Together, Z and X give you 2 of the interior angles of Triangle QPR
Thus
<QPR + Z + X = 180
<QPR + 90 = 180
<QPR = 90
C together sufficient
Of course you don’t have to do the whole calculation once you know you have enough information to find the angle
Posted from my mobile device
S1: just knowing that 2 lines are parallel doesn’t help us get exact values. The triangle formed by QPR could move around in all kinds of directions.
Not sufficient
S2: we are not given any values - it’s not possible to find a unique value
Together
Since AB and CD are parallel, line QR becomes a Transversal line intersecting the 2 parallel lines
This gives us certain unique relationships among the angles. One of those is that the “same side” interior angles are Supplementary, or they SUM to 180 degrees.
This means:
Angle <AQR + Angle < CRQ = 180 degrees
We are told that the 2 angles at point R are equal —- call each angle X so that the entire Angle <CRQ = 2X
We are also told that the 2 angles at point Q are equal —— call each angle Z so that the entire Angle <AQR = 2Z
Substitute into the equation above
2Z + 2X = 180
Z + X = 90
Together, Z and X give you 2 of the interior angles of Triangle QPR
Thus
<QPR + Z + X = 180
<QPR + 90 = 180
<QPR = 90
C together sufficient
Of course you don’t have to do the whole calculation once you know you have enough information to find the angle
Posted from my mobile device
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