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# What is the measure of angle B in triangle ABC? (1) The ratio of the

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What is the measure of angle B in triangle ABC? (1) The ratio of the  [#permalink]

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13 Sep 2018, 05:00
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25% (medium)

Question Stats:

72% (00:48) correct 28% (01:09) wrong based on 40 sessions

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What is the measure of angle B in triangle ABC?

(1) The ratio of the angles in triangle ABC is 3 : 4 : 5
(2) BC < AB < AC

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Re: What is the measure of angle B in triangle ABC? (1) The ratio of the  [#permalink]

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13 Sep 2018, 05:24
Bunuel wrote:
What is the measure of angle B in triangle ABC?

(1) The ratio of the angles in triangle ABC is 3 : 4 : 5
(2) BC < AB < AC

1) If the ratio of angles is known. We know sum of the three angles as 180.
So, 3a+4a+5a = 180. So, a could be calculated. Hence, all the three angles could be calculated, leave just B. Hence, sufficient.
2) Just by knowing that three sides are not equal, don't give any information about the exact length of sides or exact angles of a triangle. Hence, insufficient.

Hence, A.
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Re: What is the measure of angle B in triangle ABC? (1) The ratio of the  [#permalink]

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13 Sep 2018, 06:28
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Bunuel wrote:
What is the measure of angle B in triangle ABC?

(1) The ratio of the angles in triangle ABC is 3 : 4 : 5
(2) BC < AB < AC

Statement 1 - Since the sum of all angles of triangle is 180, we can calculate the individual angles using the given ratio. The angles are 75,60, and 45. Yet, this gives no information about angle B. Not sufficient.

Statement 2 - No information about angles. Not sufficient.

Using both statements together, we can say B=angle opposite to largest side=AC. So B is the largest angle, i.e 75 degs.

Hence C.

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Re: What is the measure of angle B in triangle ABC? (1) The ratio of the  [#permalink]

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13 Sep 2018, 07:43
abhishekrukhaiyar wrote:
Bunuel wrote:
What is the measure of angle B in triangle ABC?

(1) The ratio of the angles in triangle ABC is 3 : 4 : 5
(2) BC < AB < AC

1) If the ratio of angles is known. We know sum of the three angles as 180.
So, 3a+4a+5a = 180. So, a could be calculated. Hence, all the three angles could be calculated, leave just B. Hence, sufficient.
2) Just by knowing that three sides are not equal, don't give any information about the exact length of sides or exact angles of a triangle. Hence, insufficient.

Hence, A.

I think it should be C.

From stmt. 1, although we can calculate the 3 angles, we can't predict the measure of angle B per se. It could be 45 or 60 or 75.
From stmt. 2, we know side opposite to angle a (BC) < side opposite to angle c (AB) < Side opposite angle b (AC) but the measurements aren't calculable.

Using both, we know the measures and also that angle b is the largest angle.
Re: What is the measure of angle B in triangle ABC? (1) The ratio of the   [#permalink] 13 Sep 2018, 07:43
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