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In triangle ABC, if AB = BC and the degree measure
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01 Sep 2017, 11:53
01 Sep 2017, 11:53
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Question Stats:
78% (00:43) correct
21% (00:38) wrong based on 32 sessions
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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.
A) 30°
B) 75°
C) 90°
D) 120°
E) It cannot be determined from the information given.
Show: ::
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?
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?
Re: In triangle ABC, if AB = BC and the degree measure
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02 Sep 2017, 10:56
02 Sep 2017, 10:56
1
Expert Reply
Hey,
Now you have an isosceles trinagle ABC.
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!
scalene.png [ 65.8 KiB | Viewed 17079 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.
Now you have an isosceles trinagle ABC.
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!
Show: :: Img
Attachment:
scalene.png [ 65.8 KiB | Viewed 17079 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.
Re: In triangle ABC, if AB = BC and the degree measure
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14 Dec 2021, 00:55
14 Dec 2021, 00:55
Expert Reply
