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In the figure above, what is the sum of the degree measures of the mar
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23 May 2020, 06:58
23 May 2020, 06:58
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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 [ 9.6 KiB | Viewed 10050 times ]
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Re: In the figure above, what is the sum of the degree measures of the mar
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23 May 2020, 07:08
23 May 2020, 07:08
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Let two triangles be ABC and DEF with A and D over lapping each other and the points they intersect be G and H
Statement 1.
The triangles are equilateral triangle.
Hence the tip of triangles is the quadrilateral form will be of 60° each.
Sum of angles inside any quadrilateral is 360.
ADGH is also a quadrilateral.
Angle A+D+G+H = 360
60+60+G+H=360
G+H=240
(Sufficient)
Statement 2:
Perimeter of both triangles are same. (Nothing mentioned regarding angles)
Not sufficient to determine whether they are equilateral triangle, scaler, right angled or any. (Not sufficient)
Answer is A
Posted from my mobile device
Statement 1.
The triangles are equilateral triangle.
Hence the tip of triangles is the quadrilateral form will be of 60° each.
Sum of angles inside any quadrilateral is 360.
ADGH is also a quadrilateral.
Angle A+D+G+H = 360
60+60+G+H=360
G+H=240
(Sufficient)
Statement 2:
Perimeter of both triangles are same. (Nothing mentioned regarding angles)
Not sufficient to determine whether they are equilateral triangle, scaler, right angled or any. (Not sufficient)
Answer is A
Posted from my mobile device
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Re: In the figure above, what is the sum of the degree measures of the mar
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24 May 2020, 10:15
24 May 2020, 10:15
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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
Answer: A
Cheers,
Brent
