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 [ 15.45 KiB | Viewed 668 times ]
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

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