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# What is the degree measure of the largest angle in ΔPQR ?

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Re: What is the degree measure of the largest angle in ΔPQR ? [#permalink]
Bunuel
What is the degree measure of the largest angle in ΔPQR ?

(1) The degree of measure of angle P is 95.
(2) ΔPQR is isosceles.

PS21258

statement 1: The degree of measure of angle P is 95.
we know that sum of three angles of triangle is 180
<P+<Q+<R = 180
95+<Q+<R = 180
or <Q+<R = 85
now, the Max value of <Q or <R be close to 85(hypothetically)
actually, Max Value of <Q or <R will be <85
therefore, <p largest angle = 95: sufficient

statement 2: ΔPQR is isosceles
it implies two sides and their corresponding angles are equal
it can be 30-30-120 triangle
or 45-45-90 triangle
or even 70-70-40 triangle
therefore, not sufficient

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Re: What is the degree measure of the largest angle in ΔPQR ? [#permalink]
To find: largest angle in triangle PQR.

Statement 1: Angle P = 95°
Sum of angles of a triangle= 180°
⟨P+⟨Q+⟨R=180
95+⟨Q+⟨R=180
⟨Q+⟨R= 180-95
⟨Q+⟨R= 85
Now,
Let any of the two angle be 5. no matter if R is 5 or Q is 5 other angle will be 80 which is shorter than 95.
Therefore the largest angle in the ∆PQR is 95 (sufficient)

Statement 2: PQR is an isoceles triangle.
Case 1. Let two of the isoceles triangle angles be the greater one, per say 89° each. The third angle will be smaller. There is no unique greatest value for one angle of triangle PQR. There are two angle with same angle (insufficient)

Case 2: Let two angles be of 5° each.
The third angle will be 170° (sufficient)

There are two vales from statement 2, which is not giving one particular value. So statement 2 is (insufficient)

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Re: What is the degree measure of the largest angle in ΔPQR ? [#permalink]
Bunuel
What is the degree measure of the largest angle in ΔPQR ?

(1) The degree of measure of angle P is 95.
(2) ΔPQR is isosceles.

DS21258

Asked: What is the degree measure of the largest angle in ΔPQR ?

(1) The degree of measure of angle P is 95.
Sum of other angles = 180 - 95 = 85
The degree measure of the largest angle in ΔPQR = 95
SUFFICIENT

(2) ΔPQR is isosceles.
No angle measure is available
NOT SUFFICIENT

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Re: What is the degree measure of the largest angle in ΔPQR ? [#permalink]
Lets analyze the question stem, we need to find the largest angle of ΔPQR. Nothing is provided,

STATEMENT I:: The degree of measure of angle P is 95.
Sum of all angles = 180; one angle is 95; sum of remaining two angles = 180 - 95 = 85
Hence the provided angle is the largest.

SUFFICIENT. So A or D

STATEMENT II:: ΔPQR is isosceles.

This means two angles are equal but this is not sufficient to find angles. Angles can be 30, 30 or 10,10 or 45, 45 so no exact answer.
NOT SUFFICIENT

Hence A
Re: What is the degree measure of the largest angle in ΔPQR ? [#permalink]
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