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

Answer is B.

The sum of the angles of a Triangle is 180, if F is 96 that means , another angle cannot be the same as 96 because 96+96 exceeds 180.
However, we can deduce that remaining two angles are equal. so (180-96)/2 will be the value of angle E.

Statement A

<D = 42 degrees.

The remaining needs to be 180 - 42 = 138 degrees.

There could be two cases. In first case, <D is the angle that has an equal counterpart. In that case, the two angles combine to give 42 + 42 = 84 degrees. The remaining angle is 96 degrees. But which angle measures 96 degrees - E or F. Hence, this statement is insufficient.

Statement B

<F = 96 degrees.
This cannot be one of the two equal angles in the isosceles triangle as it violates the rule that sum of three angles of a triangle is equal to 180 degrees.

Hence the remaining two angles contribute to the 180 - 96 = 84 degrees. And the two equal angles are 42 degrees each. In any case, <E is equal to 42 degrees.

Hence B is sufficient.

Rules used:
1. An isosceles triangle has two equal sides and two equal angles
2. The sum of three angles of any triangle (across the Newtonian realm of existence) is 180 degree
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Statement 1:-
It doesn't specify which angles are equal.
The angles can be 42,42,96 or 42,69,69
INSUFFICIENT

Statement 2:-
Angle F is 96 degrees. It is an obtuse angle.
Sine there cannot be 2 obtuse angles in the triangle, 96 cannot be one of the equal angles.
So, the other two angles are equal with each angle measuring 42 degrees each.
SUFFICIENT

Answer:-B

In Isosceles triangle DEF, we have 3 configurations
a) DE = EF (angle D = angle F)
b) DE = DF (angle E = angle F)
c) EF= DF (angle E = angle D)

Evaluate
1) Info about only angle D is given. We don't know which of the above configuration is there for this triangle DEF. So this is INSUFFICIENT.

2) Angle F = 96.
Sum of remaining two angles will be 180 - 96 = 84*.
Now, we can't have two angles measuring 96 degrees. So the rest two angles (angle D and angle E) have to be equal; angle D = angle E = 84/2 = 42 degrees.
So this is SUFFICIENT.

Correct Answer B.

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

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


Statement 1 : D = 42
so, E + F = 180 - 42 = 138

since DEF is isosceles E and F can be equal and measure = 69
if E = F ; D = 42, E=F = 69
if D is equal to one anther angle then the third angle = 96.

two possibilities. therefore Insufficient

Statement 2 : F = 96
so, D + E = 180 - 96 = 84

since DEF is isosceles D and E can be equal and measure = 42
if F is equal to another angle then the total = 96 + 96 = 192

But sum of angles of triangle = 180.

so D = 42
Sufficient

Answer = B

IMO B,
with just 1st option, there are two possibilities
with 2nd option there is only 1 choice for other angles

IMO: B

Clearly A is not sufficient.
2(96) > 180. this condition is not possible. Therefor 96 can be one of the angles. Now other two angles can be found out. So B is sufficient

@Bunnel



Hi Bunnel

Kudos for this please

Do not ask for Kudos. If your post deserves one, Bunuel will give you 1 kudos.
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I believe the answer is B. Please see below for explanation.

0) From the question we get that triangle DEF is isosceles meaning that two sides are equal and also that two angles are equal.

(1) From statement 1 we get that Angle D measures 42 degrees

If angle D measures 42 that could mean that angle E could be 42 and angle F could be 180 - 2*42 = 96

or

If angle D measures 42 that means that angle F could be 42 and angle E could be 180 - 2*42 = 96

(2) Angle F measures 96 degrees

If angle F measures 96 degrees it means that F has to be the biggest angle, because 96+96 = 192 and that is bigger than 180. Another away to put it would be that there can't be another angle equal to 96 (Isosceles remember). With this in mind and if F is the biggest angle then the remaining angles must be (180-96)/2

Answer B

Similar question to practice: in-isosceles-triangle-rst-what-is-the-measure-of-angle-r-129378.html
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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

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