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Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
Princ wrote:
amanvermagmat wrote:
Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)



OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is \(360^{\circ}\).
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total \(2*120^{\circ} =240^{\circ}\),Third exterior angle should be also \(360^{\circ}-240^{\circ}=120^{\circ}\)
\(\angle\)P=\(\angle\)Q=\(\angle\)R= \(180^{\circ}-120^{\circ}\)(\(120^{\circ}\) being exterior angle)
\(\angle\)P=\(\angle\)Q=\(\angle\)R=\(60^{\circ}\)
Question is reduced to whether \(\triangle\)PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether \(\triangle\)PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of \(\angle\) P is not \(60^{\circ}\), so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether \(\triangle\)PQR is an equilateral triangle or not?

so OA should be D





(1) PQR is NOT an isosceles triangle.

As above statement (1) says triangle is not isosceles how can we conclude that such triangle is not equilateral :roll:

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC. :sad:
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Re: Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
GMAT215 wrote:
Princ wrote:
amanvermagmat wrote:
Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)



OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is \(360^{\circ}\).
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total \(2*120^{\circ} =240^{\circ}\),Third exterior angle should be also \(360^{\circ}-240^{\circ}=120^{\circ}\)
\(\angle\)P=\(\angle\)Q=\(\angle\)R= \(180^{\circ}-120^{\circ}\)(\(120^{\circ}\) being exterior angle)
\(\angle\)P=\(\angle\)Q=\(\angle\)R=\(60^{\circ}\)
Question is reduced to whether \(\triangle\)PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether \(\triangle\)PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of \(\angle\) P is not \(60^{\circ}\), so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether \(\triangle\)PQR is an equilateral triangle or not?

so OA should be D





(1) PQR is NOT an isosceles triangle.

As above statement (1) says triangle is not isosceles how can we conclude that such triangle is not equilateral :roll:

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC. :sad:


Hello

Its simple if we look at it this way:

If a triangle is not isosceles, then it obviously cannot be equilateral. An isosceles triangle is one where two of its sides are equal. So if a triangle has no 2 sides equal, then obviously it cannot have its all 3 sides equal. Question answered.
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Re: Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
amanvermagmat wrote:
GMAT215 wrote:
Princ wrote:
[quote="amanvermagmat"]Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)



OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is \(360^{\circ}\).
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total \(2*120^{\circ} =240^{\circ}\),Third exterior angle should be also \(360^{\circ}-240^{\circ}=120^{\circ}\)
\(\angle\)P=\(\angle\)Q=\(\angle\)R= \(180^{\circ}-120^{\circ}\)(\(120^{\circ}\) being exterior angle)
\(\angle\)P=\(\angle\)Q=\(\angle\)R=\(60^{\circ}\)
Question is reduced to whether \(\triangle\)PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether \(\triangle\)PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of \(\angle\) P is not \(60^{\circ}\), so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether \(\triangle\)PQR is an equilateral triangle or not?

so OA should be D





(1) PQR is NOT an isosceles triangle.

As above statement (1) says triangle is not isosceles how can we conclude that such triangle is not equilateral :roll:

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC. :sad:


Hello

Its simple if we look at it this way:

If a triangle is not isosceles, then it obviously cannot be equilateral. An isosceles triangle is one where two of its sides are equal. So if a triangle has no 2 sides equal, then obviously it cannot have its all 3 sides equal. Question answered.[/quote]It is given pqr is not an isoceles might be it is equlitateral which is not termed as isoceles , so how
Stment 1 suffices i also dont think so.

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Re: Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
I) triangle is not isosceles means two interior angles of triangle are not equal.
If two interior angles of triangle are not equal their exterior angles are also not equal.
Sufficient

2) P=70
Then max value of other two angles of triangle is 55 if they are isosceles
But they are not so exterior angles will not be equal to 120
Sufficient

Ans D

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Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
Exterior angle = 120 implies interior angle = 60. The only way to have 2 60 degree interior angles is to have an equilateral triangle (60, 60, 60)

1) Equilateral triangles are isosceles (two sides/angles are the same) by definition. Condition 1 negates that. Sufficient.
2) Violates condition that triangle is equilateral. Sufficient.

Alternative approach to 2)
The exterior angle of 70 is 110. The sum of the other two angles must be 110. The sum of the two exterior angles unaccounted for must be (180*2)-110 = 250, which makes it impossible to have two exterior angles of 120. Sufficient.
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Re: Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
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Re: Is the measure of two exterior angles of a triangle PQR, each equal to [#permalink]
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