M7MBA wrote: ↑

Sat Dec 18, 2021 4:15 am

In isosceles triangle \(DEF,\) what is the measure of angle \(E?\)

(1) Angle \(D\) measures \(42\) degrees.
(2) Angle \(F\) measures \(96\) degrees.

Answer: B

Source: Veritas Prep

Target question: What is the measure of ∠E?

Given: Triangle DEF is an ISOSCELES triangle
This tells us that there are 2 equal angles

Statement 1: ∠D measures 42 degrees
Here it's hard to tell whether there's a second 42-degree angle or whether the other two angles are different.
Consider these two possible cases that satisfy statement 1:
Case a: ∠D = 42°, ∠E = 42° and ∠F = 96° . In this case, the answer to the target question is ∠E = 42°
Case b: ∠D = 42°, ∠E = 69° and ∠F = 69° . In this case, the answer to the target question is ∠E = 69°
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: ∠F measures 96 degrees
In this case we KNOW that there are no other angles that measure 96 degrees.
How do we know this?
If we have a 2nd angle measuring 96 degrees, then the sum of those two angles is GREATER THAN 180°
This means the two other angles (∠D and ∠E) must be equal
So, it MUST be the case that ∠D = 42°, ∠E = 42° and ∠F = 96°
The answer to the target question is ∠E = 42°
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B