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

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Is the measure of an exterior angle of triangle XYZ equal to 140°?  [#permalink]

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New post 12 Apr 2018, 20:45
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

55% (00:58) correct 45% (01:12) wrong based on 33 sessions

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Re: Is the measure of an exterior angle of triangle XYZ equal to 140°?  [#permalink]

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New post 12 Apr 2018, 21:18
Bunuel wrote:
Is the measure of an exterior angle of triangle XYZ equal to 140°?

(1) The measure of angle Y is 60°.
(2) The measure of angle Z is 70°.


If an interior angle is 40 degrees, then the exterior angle adjacent to that interior angle will be 180-40 = 140 degrees.

(1) Exterior angle adjacent to Y = 180-60 = 120 degrees
Now its possible for another interior angle (X or Z) to be 40 degrees, but its not necessary. So we cannot say whether there is an exterior angle of 140 degrees or not.
Not sufficient.

(2) Exterior angle adjacent to Z = 180-10 = 110 degrees
Now its possible for another interior angle (Y or X) to be 40 degrees, but its not necessary. So we cannot say whether there is an exterior angle of 140 degrees or not.
Not sufficient.

Combining the statements,
Two angles are 60 and 70 so third angle must be 50 degrees. None of the three exterior angles is of 140 degrees measure. Sufficient.

Hence C answer
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Is the measure of an exterior angle of triangle XYZ equal to 140°?  [#permalink]

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New post 12 Apr 2018, 21:18
Bunuel wrote:
Is the measure of an exterior angle of triangle XYZ equal to 140°?

(1) The measure of angle Y is 60°.
(2) The measure of angle Z is 70°.


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°

Case 1: 70 - 70 - 40 i..e. Sum of two angles may be 140
Case 2: 70 - 80 - 30 i..e. Sum of two angles may NOT be 140

NOT SUFFICIENT

Combining the two statements

Two angles are 60 and 70 i.e. third angle will be 50 i.e. sum of none of the two angles is 140 hence no exterior angles is 140

SUFFICIENT

Answer: option C
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Is the measure of an exterior angle of triangle XYZ equal to 140°?

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