-
didieravoaka
- Master | Next Rank: 500 Posts
- Posts: 163
- Joined: Tue Jan 13, 2015 11:44 am
- Thanked: 2 times
IMPORTANT: In an isosceles triangle there are 2 IDENTICAL angles, and 1 LONE angle.In isosceles ∆RST, what is measure of ∠R?
1) ∠T = 100 degrees
2) ∠S = 40 degrees
Target question: What is measure of ∠R?
Statement 1: ∠T = 100 degrees
We should recognize that ∠T CANNOT be one of the identical angles. If this were the case, we'd have two angles with measures of 100 degrees each, which would result in a triangle in which the sum of the angles is GREATER than 180 degree (which is IMPOSSIBLE)
So, we can conclude that ∠T must be the LONE angle, which means ∠R and ∠S are the two IDENTICAL angles.
Since the sum of the 3 angles must be 180, we can conclude that ∠R = 40, ∠S = 40, and ∠T = 100
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: ∠S = 40 degrees
Here are two possible cases to consider:
Case a: ∠S is the LONE angle, in which case the ∠R = 70, ∠S = 40, and ∠T = 70
Case b: ∠S is one of the IDENTICAL angles, in which case we could have ∠R = 40, ∠S = 40, and ∠T = 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
