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In triangle ABC, if AB = BC and the degree measure

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In triangle ABC, if AB = BC and the degree measure [#permalink] New post 01 Sep 2017, 11:53
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Question Stats:

66% (00:05) correct 33% (00:21) wrong based on 3 sessions
In triangle ABC, if AB = BC and the degree measure of one angle is 30°, what is the greatest possible degree measure of any angle in triangle ABC?

A) 30°
B) 75°
C) 90°
D) 120°
E) It cannot be determined from the information given.

[Reveal] Spoiler:
Answer D

I know it may sound a stupid question, but I thought that E was the right option. We cannot determine the greatest possible measure because it can be 75 or 120. Am I Wrong?
[Reveal] Spoiler: OA
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Re: In triangle ABC, if AB = BC and the degree measure [#permalink] New post 02 Sep 2017, 10:56
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Hey,

Now you have an isosceles trinagle ABC.

Image

Now the angles ACB and ABC are equal. If one of the angle is given to be 30 degrees. There are two possibilities:

Case 1: \(\angle ACB = \angle ACB =30\). In this case \(\angle BAC = 180 -30 -30= 120.\)

Case 2: \(\angle BAC = 30\). In this case \(\angle ACB = \angle ACB =\frac{180 -30}{2}=75\)


These are the only two possible cases. Since case 1 has the higer value of the maximum angle hence option D is correct!
[Reveal] Spoiler: Img
Attachment:
scalene.png
scalene.png [ 65.8 KiB | Viewed 1781 times ]



PS: You figured the solution correctly. When they say highest possible value, they mean of all the possible cases the maximum possible is the answer they expect.
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Sandy
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Re: In triangle ABC, if AB = BC and the degree measure   [#permalink] 02 Sep 2017, 10:56
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