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

Question

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

eakabuah · Answer

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.

Posted from my mobile device

Archit3110 · Answer

angle b=c = 2x+x+x=180 ; x =45
so exterior angle of c ; 180-45 ; 135
IMO b

ScottTargetTestPrep · Answer

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

Sr1994 · Answer

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

Harsh9676 · Answer

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 * >> 2>>

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards