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# Is the measure of an exterior angle of a scalene triangle ABC equal to

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DS Forum Moderator
Joined: 21 Aug 2013
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Location: India
Is the measure of an exterior angle of a scalene triangle ABC equal to  [#permalink]

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12 Apr 2018, 21:33
1
00:00

Difficulty:

55% (hard)

Question Stats:

29% (00:04) correct 71% (01:01) wrong based on 20 sessions

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Is the measure of an exterior angle of a scalene triangle ABC equal to 140°? (A scalene triangle is one where no two of the three sides are equal)

(1) The measure of angle B is 60°.
(2) The measure of angle C is 70°.

(Inspired by a Bunuel's question)
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Re: Is the measure of an exterior angle of a scalene triangle ABC equal to  [#permalink]

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12 Apr 2018, 21:41
amanvermagmat wrote:
Is the measure of an exterior angle of a scalene triangle ABC equal to 140°? (A scalene triangle is one where no two of the three sides are equal)

(1) The measure of angle B is 60°.
(2) The measure of angle C is 70°.

(Inspired by a Bunuel's question)

CONCEPT: Exterior angle in a triangle = Sum of other two interior angles in the triangle

Question : Is the measure of an exterior angle of triangle XYZ equal to 140°?

i.e. Is the sum of any two angles in the triangle = 140º?

Statement 1: The measure of angle Y is 60°

Sum of the two angles in triangle may be 120 but one of the angles may be 80 to make 60+80 = 140 hence

there is no Certainty whether the sum of the two snagles i s 140 or NOT hence

Case 1: 60 - 80 - 40 i..e. Sum of two angles may be 140
Case 2: 60 - 90 - 30 i..e. Sum of two angles may NOT be 140

NOT SUFFICIENT

Statement 2: The measure of angle Z is 70°

The only possibility of sum of two angles to be 140º as per this case is 70 - 70 - 40 BUT THIS CASE IS NOT ACCEPTABLE BECAUSE SCALENE TRIANGLE HAS ALL ANGLES DIFFERENT

I.e. Sum of the two angles CAN NOT be 140º Hence

SUFFICIENT

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Re: Is the measure of an exterior angle of a scalene triangle ABC equal to &nbs [#permalink] 12 Apr 2018, 21:41
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