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# In the figure above, what is the sum of the degree measures of the mar

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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
BrentGMATPrepNow wrote:
Bunuel wrote:

In the figure above, what is the sum of the degree measures of the marked angles?

(1) The two overlapping triangles are equilateral.
(2) The two overlapping triangles have equal perimeters.
DS21268
Attachment:
1.png

Target question: What is the sum of the degree measures of the marked angles?

Statement 1: The two overlapping triangles are equilateral.
All three angles in an equilateral triangle are 60°
So are overlapping triangles look like this:

From here, if we let x and y represent the two marked angles, we get the following:

Now let's examine the quadrilateral that exists in the intersection of the two triangles
Since angles in a triangle must add to 360°, we can write: 60° + x° + 60° + y° = 360°
Simplify: x° + y° + 120°= 360°
Solve to get: x° + y° = 240°
In other words, the sum of the marked angles = 240°
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The two overlapping triangles have equal perimeters.
This information is not sufficient.
Consider these two possible cases:

Case a: The two triangles are identical equilateral triangles.
In this case, we get the same diagram we examined and statement 1:

Here, the answer to the target question is the sum of the marked angles = 240°

Case b: One triangle is an equilateral triangle, and the other is a 30-60-90 triangle with the same perimeter.
We get:

Since angles in a triangle must add to 360°, we can write: 30° + x° + 60° + y° = 360°
Simplify: x° + y° + 90°= 360°
Solve to get: x° + y° = 270°
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent

How can the perimeter of an equilateral triangle be equal to the 30-60-90? can you please help me with this? If we assume the side length to be x the perimeter of the equilateral triangle will be 3x and the same for 30-60-90 will be 3x+square root of 3x. which will be bigger than that.
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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
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agar123 wrote:
quote]
How can the perimeter of an equilateral triangle be equal to the 30-60-90? can you please help me with this? If we assume the side length to be x the perimeter of the equilateral triangle will be 3x and the same for 30-60-90 will be 3x+square root of 3x. which will be bigger than that.

What 30-60-90 right triangle are you referring to?
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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
BrentGMATPrepNow wrote:
agar123 wrote:
quote]
How can the perimeter of an equilateral triangle be equal to the 30-60-90? can you please help me with this? If we assume the side length to be x the perimeter of the equilateral triangle will be 3x and the same for 30-60-90 will be 3x+square root of 3x. which will be bigger than that.

What 30-60-90 right triangle are you referring to?

I was referring to case B for statement 2. There may be a gap in my understanding, I will highly appreciate if you can help me with this.

Case b: One triangle is an equilateral triangle, and the other is a 30-60-90 triangle with the same perimeter.
We get:
Image
Since angles in a triangle must add to 360°, we can write: 30° + x° + 60° + y° = 360°
Simplify: x° + y° + 90°= 360°
Solve to get: x° + y° = 270°
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
Top Contributor
agar123 wrote:
BrentGMATPrepNow wrote:
agar123 wrote:
quote]
How can the perimeter of an equilateral triangle be equal to the 30-60-90? can you please help me with this? If we assume the side length to be x the perimeter of the equilateral triangle will be 3x and the same for 30-60-90 will be 3x+square root of 3x. which will be bigger than that.

What 30-60-90 right triangle are you referring to?

I was referring to case B for statement 2. There may be a gap in my understanding, I will highly appreciate if you can help me with this.

Case b: One triangle is an equilateral triangle, and the other is a 30-60-90 triangle with the same perimeter.
We get:
Image
Since angles in a triangle must add to 360°, we can write: 30° + x° + 60° + y° = 360°
Simplify: x° + y° + 90°= 360°
Solve to get: x° + y° = 270°
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

An equilateral triangle can have the same perimeter as ANY shape.
For example, if the perimeter of the 30-60-90 triangle is 12 inches, then an equilateral triangle with sides of length 4 inches will have the same perimeter.
Similarly, if the perimeter of the 30-60-90 triangle is 15 miles, then an equilateral triangle with sides of length 5 miles will have the same perimeter.
In general, if the perimeter of the 30-60-90 triangle is k units, then an equilateral triangle with sides of length k/3 units will have the same perimeter.

Does that help?
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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
BrentGMATPrepNow wrote:
agar123 wrote:
BrentGMATPrepNow wrote:
agar123 wrote:
quote]
How can the perimeter of an equilateral triangle be equal to the 30-60-90? can you please help me with this? If we assume the side length to be x the perimeter of the equilateral triangle will be 3x and the same for 30-60-90 will be 3x+square root of 3x. which will be bigger than that.

What 30-60-90 right triangle are you referring to?

I was referring to case B for statement 2. There may be a gap in my understanding, I will highly appreciate if you can help me with this.

Case b: One triangle is an equilateral triangle, and the other is a 30-60-90 triangle with the same perimeter.
We get:
Image
Since angles in a triangle must add to 360°, we can write: 30° + x° + 60° + y° = 360°
Simplify: x° + y° + 90°= 360°
Solve to get: x° + y° = 270°
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

An equilateral triangle can have the same perimeter as ANY shape.
For example, if the perimeter of the 30-60-90 triangle is 12 inches, then an equilateral triangle with sides of length 4 inches will have the same perimeter.
Similarly, if the perimeter of the 30-60-90 triangle is 15 miles, then an equilateral triangle with sides of length 5 miles will have the same perimeter.
In general, if the perimeter of the 30-60-90 triangle is k units, then an equilateral triangle with sides of length k/3 units will have the same perimeter.

Does that help?

Got it. As per statement 2, the perimeter of both the triangles is the same. Nowhere it has mentioned that the side of an equilateral triangle(for eg. S) is equal to the side of the overlapping triangle corresponding to a 30-degree angle.(i.e 30-60-90 dimension will be s, square root 3s, 2s). Thanks for your reply. I am not sure, how and why I just took x in both the cases and calculated the perimeter.
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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
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Re: In the figure above, what is the sum of the degree measures of the mar [#permalink]
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