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ABC is isosceles and angle ABC =55

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Carcass
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ABC is isosceles and angle ABC =55 [#permalink] New post   25 Aug 2020, 10:41
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\(\triangle ABC\) is isosceles and \(\angle ABC =55°\)


Quantity A
Quantity B
The sum of the measures of the two angles of \(\triangle ABC\) that have equal measure
\( 115°\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: ABC is isosceles and angle ABC =55 [#permalink] New post   25 Aug 2020, 10:42
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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fraise
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Re: ABC is isosceles and angle ABC =55 [#permalink] New post   25 Aug 2020, 12:49
2
We need more information to know whether quantity A is greater or not.
Indeed, the fact that ABC is an isoceles triangle only tells us that two angles (the "base angles") are equal. Two cases arise:
- Either the two equal angles both have value of 55°, then the sum of the two angles that have equal measure is 105° thus A<B
- Or the angle with measure 55° is not one of the base angles, and the two equal angles have another measure. To find the measure of the angle, denoted by x, we know that the sum of the three angles is 180. So the three angles verify: 2x+55°=180 that is 2x=125. Then A>B.
So we cannot conclude.
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Re: ABC is isosceles and angle ABC =55 [#permalink] New post   Updated on: 26 Aug 2020, 08:29
180-55=125>115 degrees

I am surprised the question is designated as hard.

Originally posted by AenElle on 26 Aug 2020, 08:27.
Last edited by AenElle on 26 Aug 2020, 08:29, edited 1 time in total.
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Re: ABC is isosceles and angle ABC =55 [#permalink] New post   26 Aug 2020, 08:28
fraise wrote:
We need more information to know whether quantity A is greater or not.
Indeed, the fact that ABC is an isoceles triangle only tells us that two angles (the "base angles") are equal. Two cases arise:
- Either the two equal angles both have value of 55°, then the sum of the two angles that have equal measure is 105° thus A<B
- Or the angle with measure 55° is not one of the base angles, and the two equal angles have another measure. To find the measure of the angle, denoted by x, we know that the sum of the three angles is 180. So the three angles verify: 2x+55°=180 that is 2x=125. Then A>B.
So we cannot conclude.



Actually, you are wrong. It doesn't say any angle in the triangle is equal to 55 degrees - it says that the specific angle (the one with the vertex B) has a value of 55 degrees. So, the answer is A.
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Re: ABC is isosceles and angle ABC =55 [#permalink] New post   26 Aug 2020, 09:29
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AenElle wrote:
180-55=125>115 degrees

I am surprised the question is designated as hard.


Medium - hard

It is quite different
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Re: ABC is isosceles and angle ABC =55 [#permalink] New post   26 Aug 2020, 10:41
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Carcass wrote:
\(\triangle ABC\) is isosceles and \(\angle ABC =55°\)


Quantity A
Quantity B
The sum of the measures of the two angles of \(\triangle ABC\) that have equal measure
\( 115°\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


We have two cases for the angles of this isosceles.

Case 1) Angles: \(x°, x°\) and \(55°\)
The sum of measures of two congruent angles is \(A = x° + x° = 180° - 55° = 125° > 115°\).
Thus, we have \(A > B\).

Case 2) Angles: \(55°, 55°\) and \(y°\)
The sum of measures of two congruent angles is \(A = 55° + 55° = 110° < 115°\).
Thus, we have \(A < B\).

Therefore, D is the right answer.
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Re: ABC is isosceles and angle ABC =55 [#permalink]
26 Aug 2020, 10:41
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