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Re: In isosceles triangle DEF, what is the measure of angle E?
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22 Sep 2015, 03:49
1
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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.
In isosceles triangle DEF, what is the measure of angle E?
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22 Sep 2015, 04:25
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 _________________
Re: In isosceles triangle DEF, what is the measure of angle E?
[#permalink]
22 Sep 2015, 10:02
1
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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
Re: In isosceles triangle DEF, what is the measure of angle E?
[#permalink]
22 Sep 2015, 11:49
1
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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. _________________
It ain’t about how hard you hit. It’s about how hard you can get hit and keep moving forward; how much you can take and keep moving forward. That’s how winning is done!
In isosceles triangle DEF, what is the measure of angle E?
[#permalink]
23 Sep 2015, 07:30
1
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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
Re: In isosceles triangle DEF, what is the measure of angle E?
[#permalink]
28 Sep 2015, 02:25
@Bunnel
vivekgautam1 wrote:
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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.
Hi Bunnel
Kudos for this please _________________
It ain’t about how hard you hit. It’s about how hard you can get hit and keep moving forward; how much you can take and keep moving forward. That’s how winning is done!
Re: In isosceles triangle DEF, what is the measure of angle E?
[#permalink]
28 Sep 2015, 02:50
vivekgautam1 wrote:
@Bunnel
vivekgautam1 wrote:
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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.
Hi Bunnel
Kudos for this please
Do not ask for Kudos. If your post deserves one, Bunuel will give you 1 kudos. _________________
Re: In isosceles triangle DEF, what is the measure of angle E?
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29 Sep 2015, 10:39
1
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
In isosceles triangle DEF, what is the measure of angle E?
[#permalink]
12 Dec 2018, 13:45
1
Top Contributor
Expert Reply
Bunuel wrote:
In isosceles triangle DEF, what is the measure of angle E?
(1) Angle D measures 42 degrees (2) Angle F measures 96 degrees
Kudos for a correct solution.
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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Re: In isosceles triangle DEF, what is the measure of angle E?
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16 Jan 2020, 10:42
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