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

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Bunuel
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In triangle ABC, AB=AC and the measure of angle A is twice the measure [#permalink] New post   07 Aug 2019, 02:19
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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] New post   07 Aug 2019, 03:04
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

The answer is therefore B.

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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure [#permalink] New post   08 Aug 2019, 12:27
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] New post   12 Aug 2019, 11:58
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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


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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Re: In triangle ABC, AB=AC and the measure of angle A is twice the measure [#permalink] New post   27 Oct 2020, 09:14
Since AB =AC, it's an Isosceles triangle.

let's take the angle as B

So, 2B+B+B = 180
4B = 180
B = 45

Therefore External angle of C = 180 - 45 = 135

Answer B
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In triangle ABC, AB=AC and the measure of angle A is twice the measure [#permalink] New post   27 Oct 2020, 10:48
IMO B

Exterior angle = Sum of opposite two interior angles.

Given AB = AC, therefore triangle ABC would wither be an Isosceles or an Equilateral Triangle.

Also < A = 2 * <B, which implies ABC is an Isosceles triangle (Since in Equilateral triangle all the interior angles are equal)

We can also deduce that <B = <C ( since in Isosceles triangle, interior angles of equal sides are equal)

Therefore <A + <B + <C = 180 >>> 2<B + <B + <B = 180 >>> <B = 45

therefore Exterior angle of C = <B + <A
= <B + 2 <B
= 3 (45)
= 135 degrees
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In triangle ABC, AB=AC and the measure of angle A is twice the measure [#permalink]
27 Oct 2020, 10:48
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