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 ΔPQRAPPROACH #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 ΔPQRSince 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 ΔPQRCase 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 ΔPQRSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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