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

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

Answer: A

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)

Answer is A

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

Statement 1: The degree of measure of ∠P is 95.
APPROACH #1: Logic
Since angles in a triangle add to 180 degrees, it's impossible for any other angles to be greater than 95 degrees (otherwise the sum of the three angles will be greater than 180 degrees)
So it must be the case that 95 degrees is the largest angle in ΔPQR

APPROACH #2: Algebra
Since angles in a triangle must add to 180 degrees, we know that ∠P + ∠Q + ∠R = 180
Substitute to get: 95 + ∠Q + ∠R = 180
Subtract 95 from both sides to get: ∠Q + ∠R = 85
If the SUM of ∠Q and ∠R is 85, neither angle can be greater than 85.
So it must be the case that 95 degrees is the measure of the largest angle in ΔPQR

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ΔPQR is isosceles.
There are tons of isosceles triangles that satisfy statement 2. Here are two:
Case a: ΔPQR has angle measurements 30-30-120. In this case, the answer to the target question is 120 degrees is the measure of the largest angle in ΔPQR
Case b: ΔPQR has angle measurements 40-40-100. In this case, the answer to the target question is 100 degrees is the measure of the largest angle in ΔPQR
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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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

IMO A

Lets analyze the question stem, we need to find the largest angle of ΔPQR. Nothing is provided,
let's jump to statements analysis.

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
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In any triangle if one angle is more than 90 then we don't have to think for the largest angle and we can just choose that angle as the largest angle.
WHY??
This is because sum of all the interior angles of a triangle is equal to 180 degree when we know one of the angle is more than 90 then sum of other two angles has to be less than 90.
in case you are still confused then just consider this question where it is provided that angle P is 95 now think of what maximum value can either Q or R can assume.
you'll say angle of Q/R has to be less than 85
lets say Q is 84 and R is 1 now you will appreciate the first statement of this answer.