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# In the figure above, when ray OA is rotated clockwise 9 degrees about

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Math Expert
Joined: 02 Sep 2009
Posts: 55265
In the figure above, when ray OA is rotated clockwise 9 degrees about  [#permalink]

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01 Aug 2017, 04:39
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Difficulty:

15% (low)

Question Stats:

88% (00:39) correct 12% (00:35) wrong based on 34 sessions

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In the figure above, when ray OA is rotated clockwise 9 degrees about point O, then it will be perpendicular to ray OB. What is the measure of ∠AOB before rotation?

(A) 81°
(B) 89°
(C) 99°
(D) 93°
(E) 90°

Attachment:

2017-08-01_1347_002.png [ 4.3 KiB | Viewed 828 times ]

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In the figure above, when ray OA is rotated clockwise 9 degrees about  [#permalink]

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06 Aug 2017, 12:03
1
Bunuel wrote:

In the figure above, when ray OA is rotated clockwise 9 degrees about point O, then it will be perpendicular to ray OB. What is the measure of ∠AOB before rotation?

(A) 81°
(B) 89°
(C) 99°
(D) 93°
(E) 90°

Attachment:
The attachment 2017-08-01_1347_002.png is no longer available

Attachment:

ray-angle-change.png [ 17.98 KiB | Viewed 619 times ]

If ray OA is perpendicular to OB after rotation, ∠AOB is 90 degrees.

If need be, draw the end result (in diagram, where OA is red) to track on ray's movement.

Original ray OA is rotated clockwise 9 degrees: it moves from left to right 9 degrees.

Measure of ∠AOB before rotation? It "shrank." So add: 90 + 9 = 99 degrees.

You can do this problem with compass (absolute bearing and relative bearing) or clock angles; IMO, unnecessarily complicated. YMMV.

Edited for a typo that created a grammatical mistake which could cause problems in SC. Answer remains the same.
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In the figure above, when ray OA is rotated clockwise 9 degrees about   [#permalink] 06 Aug 2017, 12:03
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