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

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

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

Cheers,
Brent
RELATED VIDEO

Originally posted by BrentGMATPrepNow on 24 May 2020, 10:56.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:32, edited 1 time in total.
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Re: What is the degree measure of the largest angle in ΔPQR ? [#permalink]
Bunuel wrote:
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

IMO A
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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
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What is the degree measure of the largest angle in ΔPQR ? [#permalink]
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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.
What is the degree measure of the largest angle in ΔPQR ? [#permalink]