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# In triangle ABC, AB=AC and the measure of angle A is twice the measure

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Math Expert
Joined: 02 Sep 2009
Posts: 64172
In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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07 Aug 2019, 01:19
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Difficulty:

25% (medium)

Question Stats:

81% (01:18) correct 19% (01:29) wrong based on 63 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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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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07 Aug 2019, 02:04
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

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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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08 Aug 2019, 11:27
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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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure  [#permalink]

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12 Aug 2019, 10:58
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.

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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure   [#permalink] 12 Aug 2019, 10:58