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Math Expert V
Joined: 02 Sep 2009
Posts: 57155
In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 84% (01:12) correct 16% (01:28) wrong based on 49 sessions

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In triangle ABC, AB=AC and the measure of angle A is twice the measure of angle B. Find the number of degrees in the measures of the exterior angle at C.

(A) 145 degrees
(B) 135 degrees
(C) 125 degrees
(D) 95 degrees
(E) 45 degrees

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Manager  G
Joined: 18 May 2019
Posts: 154
Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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We know that triangle ABC has AB=AC implying triangle ABC is an isosceles triangle. This means angle at edge B equals angle at edge C. We also know from the question that angle at edge A is two times angle at edge B. Let x be the angle at edge A. Then angle at edge B and C=x/2
We can therefore write this equation for the angles: x+x/2 + x/2=180
2x=180
x=90.
x/2=B=C=45
The exterior angle at C = 180-45=135

The answer is therefore B.

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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4491
Location: India
Concentration: Sustainability, Marketing
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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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Bunuel wrote:
In triangle ABC, AB=AC and the measure of angle A is twice the measure of angle B. Find the number of degrees in the measures of the exterior angle at C.

(A) 145 degrees
(B) 135 degrees
(C) 125 degrees
(D) 95 degrees
(E) 45 degrees

angle b=c = 2x+x+x=180 ; x =45
so exterior angle of c ; 180-45 ; 135
IMO b
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Target Test Prep Representative D
Status: Founder & CEO
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Joined: 14 Oct 2015
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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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1
Bunuel wrote:
In triangle ABC, AB=AC and the measure of angle A is twice the measure of angle B. Find the number of degrees in the measures of the exterior angle at C.

(A) 145 degrees
(B) 135 degrees
(C) 125 degrees
(D) 95 degrees
(E) 45 degrees

Since AB = AC, triangle ABC is an isosceles triangle with base angles at B and C and vertex angle at A. Since the base angles of an isosceles triangle are equal in measure, we can let angle B = angle C = x, and thus angle A = 2x. Since the three angles of a triangle sum to 180, we can create the equation:

x + x + 2x = 180

4x = 180

x = 45

Thus, angle C = 45 and the exterior angle at C is 180 - 45 = 135.

Answer: B
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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure   [#permalink] 12 Aug 2019, 11:58
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# In triangle ABC, AB=AC and the measure of angle A is twice the measure

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