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505-555 (Easy)|   Geometry|      
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Bunuel
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In a triangle, the ratio of two angles is 5:2, and the third angle is 31 Jan 2016, 07:44
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80% (01:15) correct 20% (01:25) wrong based on 74 sessions

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In a triangle, the ratio of two angles is 5:2, and the third angle is equal to the difference between the other two. What is the number of degrees in the smallest angle?

A. 18
B. 25 2⁄7
C. 25 5⁄7
D. 36
E. 54
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D
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chetan2u
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In a triangle, the ratio of two angles is 5:2, and the third angle is 31 Jan 2016, 08:05
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Bunuel
In a triangle, the ratio of two angles is 5:2, and the third angle is equal to the difference between the other two. What is the number of degrees in the smallest angle?

A. 18
B. 25 2⁄7
C. 25 5⁄7
D. 36
E. 54
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At first it may seem that the info is not sufficient, but if we look, we have been provided with some info about each angle..

the ratio of two angles is 5:2..
let the common ratio between the two angles be x..
so angles are 5x and 2x..
the third angle is the difference of these 2, so it is 5x-2x=3x..

so we have all three angles as 2x,3x, and 5x..
so 2x+3x+5x=180..
x=18..

After doing everything correctly, we should an extra second to look for what is asked and answer accordingly..
smallest angle=2x=2*18=36..
D
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In a triangle, the ratio of two angles is 5:2, and the third angle is 31 Jan 2016, 21:20
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Bunuel
In a triangle, the ratio of two angles is 5:2, and the third angle is equal to the difference between the other two. What is the number of degrees in the smallest angle?

A. 18
B. 25 2⁄7
C. 25 5⁄7
D. 36
E. 54
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Let the two angles be 5x and 2x.
Third angle = 5x - 2x = 3x.

Sum of three angles = 10x = 180
Hence x = 18.

Smallest angle = 36.
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In a triangle, the ratio of two angles is 5:2, and the third angle is 02 Feb 2016, 23:57
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Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that, In a triangle, the ratio of two angles is 5:2, and the third angle is equal to the DIFFERENCE between the other two. We're asked for the number of degrees in the smallest angle.

Since the ratio of two of the angles is 5:2, the first angle will be some multiple of 5 and the second will be the equivalent multiple of 2. By extension, the third angle will be an equivalent multiple of 3. Since we're asked to find the measure of the smallest angle, and the answers are all numbers, we can TEST THE ANSWERS.

Let's TEST Answer D:

IF...
the smallest angle = 36
2(18) = 36
5(18) = 90
the largest angle = 90
90 - 36 = 54
the third angle = 54
36+54+90 = 180, so this is a triangle and this matches everything we were told. This MUST be the answer.

Final Answer:
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D

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In a triangle, the ratio of two angles is 5:2, and the third angle is 04 Feb 2016, 02:49
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Bunuel
In a triangle, the ratio of two angles is 5:2, and the third angle is equal to the difference between the other two. What is the number of degrees in the smallest angle?

A. 18
B. 25 2⁄7
C. 25 5⁄7
D. 36
E. 54
Show more

Assume the angles to be 5x and 2x
We have been told that the remaining angle = 5x - 2x = 3x

Now we know that the sum of angles of a triangle = 180
Therefore 5 x + 2x + 3x + 180
10x = 180

Hence x = 18
Of 5x, 2x and 3x, 2x is the smallest.
Hence the smallest angle = 2*18 = 36 (Option D)
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In a triangle, the ratio of two angles is 5:2, and the third angle is 22 Oct 2020, 12:57
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