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In the figure above, if angle AQR = 145°, and angle BQP = 122°, then

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In the figure above, if angle AQR = 145°, and angle BQP = 122°, then [#permalink]

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New post 17 Aug 2017, 23:51
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In the figure above, if angle AQR = 145°, and angle BQP = 122°, then the degree measure of angle PQR =

(A) 87
(B) 88
(C) 89
(D) 90
(E) 91


[Reveal] Spoiler:
Attachment:
2017-08-18_1028_003.png
2017-08-18_1028_003.png [ 9.06 KiB | Viewed 285 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, if angle AQR = 145°, and angle BQP = 122°, then [#permalink]

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New post 18 Aug 2017, 00:13
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In the figure above, if angle AQR = 145°
Since in the straight line, angle AQR + BQR = 180°
Therefore, Angle BQR = 180 - 145 = 35

Similarly, we know that angle BQP = 122°,
Since in the straight line, angle AQP + BQP = 180°
Therefore, Angle BQP = 180 - 122 = 58

The degree measure of angle PQR + BQP + BQR = 180(since angle in a straight line is 180 degree)
Therefore, PQR = 180 - (35+58) = 180 - 93 = 87(Option A)
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Re: In the figure above, if angle AQR = 145°, and angle BQP = 122°, then [#permalink]

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New post 18 Aug 2017, 01:02
Bunuel wrote:
Image
In the figure above, if angle AQR = 145°, and angle BQP = 122°, then the degree measure of angle PQR =

(A) 87
(B) 88
(C) 89
(D) 90
(E) 91


[Reveal] Spoiler:
Attachment:
2017-08-18_1028_003.png


AQR = 145 => BQR = 180-145 = 35
BQP = 122 => AQP = 180-122 = 58
PQR+BQR+AQP = 180
PQR = 180-35-58 = 87
A
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Re: In the figure above, if angle AQR = 145°, and angle BQP = 122°, then [#permalink]

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New post 18 Aug 2017, 01:52
Ans : a

AQR and BQR are supplementary . (sum up to 180 )

Thus BQR = 180-145 = 35

Similarly AQP = 180-122 = 58

AQP+PQR+BQR = 180 . Thus putting the values PQR = 87

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Re: In the figure above, if angle AQR = 145°, and angle BQP = 122°, then   [#permalink] 18 Aug 2017, 01:52
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In the figure above, if angle AQR = 145°, and angle BQP = 122°, then

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