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In triangle ABC, AB=BC and (C's measure is 65°. ) What is the measure

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In triangle ABC, AB=BC and (C's measure is 65°. ) What is the measure  [#permalink]

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New post 08 Aug 2019, 01:33
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Re: In triangle ABC, AB=BC and (C's measure is 65°. ) What is the measure  [#permalink]

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New post 08 Aug 2019, 03:48
Bunuel wrote:
In triangle ABC, AB=BC and C's measure is 65°. What is the measure of angle B?

A. 40°
B. 50°
C. 60°
D. 65°
E. 75°


Given: In triangle ABC, AB=BC and C's measure is 65°.

Asked: What is the measure of angle B?

AB=BC => Angle A = Angle C = 65°
For a triangle, sum of all 3 angles = 180°
2*65+B = 180
B=50°

IMO B
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Re: In triangle ABC, AB=BC and (C's measure is 65°. ) What is the measure  [#permalink]

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New post 08 Aug 2019, 04:40
Bunuel wrote:
In triangle ABC, AB=BC and C's measure is 65°. What is the measure of angle B?

A. 40°
B. 50°
C. 60°
D. 65°
E. 75°


Since the triangle is an isosceles triangle(AB = BC). Angles opposite to sides AB(∠C) and BC(∠A) would also be equal. We need to find ∠B.
As, ∠C = 65⁰
 ∠B = 65⁰

We know sum of all the angles of a triangle = 180⁰
 ∠A + ∠B + ∠C = 180⁰
 ∠B = 180⁰ - (∠A + ∠C)
 ∠B = 180⁰ - (65⁰ + 65⁰)
 ∠B = 180⁰ - 130⁰
 ∠B = 50⁰

Answer (B)
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Re: In triangle ABC, AB=BC and (C's measure is 65°. ) What is the measure   [#permalink] 08 Aug 2019, 04:40
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