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In the equilateral triangle RST above, y equals

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In the equilateral triangle RST above, y equals [#permalink]

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New post 24 Aug 2017, 23:43
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In the equilateral triangle RST above, y equals

(A) 60
(B) 70
(C) 75
(D) 80
(E) 85

[Reveal] Spoiler:
Attachment:
2017-08-25_1040.png
2017-08-25_1040.png [ 8.6 KiB | Viewed 628 times ]
[Reveal] Spoiler: OA

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Re: In the equilateral triangle RST above, y equals [#permalink]

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New post 25 Aug 2017, 00:28
Bunuel wrote:
Image
In the equilateral triangle RST above, y equals

(A) 60
(B) 70
(C) 75
(D) 80
(E) 85

[Reveal] Spoiler:
Attachment:
2017-08-25_1040.png

x=60/3=20
y= x+angleSRT = 20+60 = 80
D
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In the equilateral triangle RST above, y equals [#permalink]

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New post 25 Aug 2017, 11:32
Bunuel wrote:
Image
In the equilateral triangle RST above, y equals

(A) 60
(B) 70
(C) 75
(D) 80
(E) 85

[Reveal] Spoiler:
Attachment:
2017-08-25_1040.png

Sum of angles

1. x = 20

Because ∆ RST is equilateral, ∠ R, ∠ S, and ∠ T = 60

∠ S = 60 = 3x
x = 20

2. ∠ R = 60, from above

3. For leftmost small triangle, sum of angles equals 180:

x + ∠ R + third angle = 180
20 + 60 + third angle = 180
Third angle = 100
Call third angle z

4. y equals?

y and z are on a straight line
y + z = 180
y + 100 = 180
y = 80

Exterior angle

1. y = exterior angle

For small triangle on the far left with one side RS, exterior angle y = sum of interior angles x + ∠ R

2. Angles R and x

Because ∆ RST is equilateral, ∠ R, ∠ S, and ∠ T = 60

∠ R = 60

∠ S = 60 = 3x, so

x = 20

3. y equals?

y = x + ∠ R
y = 20 + 60
y = 80

Answer D

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Re: In the equilateral triangle RST above, y equals [#permalink]

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New post 25 Aug 2017, 11:49
Image

Since RST is an equilateral triangle, Angle R = S = T = 60
This implies 3x = 60 -> x = 20

If the two points on RT are A and B,
In triangle SBT, if the third angle is B
x + 60 + B = 180
Since x = 20, B = 120 - x = 120 - 20 = 1000

Therefore, in triangle SAB, the angle adjacent to B is 80
(since the sum of angles along a straight line is 180)

We know that the sum of angles in the triangle SAB is equal to 180
x + y + 80 = 180
y = 100 - x = 100 - 20 = 80(Option D)

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Re: In the equilateral triangle RST above, y equals [#permalink]

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New post 29 Aug 2017, 17:24
Bunuel wrote:
Image
In the equilateral triangle RST above, y equals

(A) 60
(B) 70
(C) 75
(D) 80
(E) 85

[Reveal] Spoiler:
Attachment:
2017-08-25_1040.png



Each of the 3 angles of an equilateral triangle has a 60-degree measure. Since angle RST = 60 degrees, 3x = 60 or x = 20. Furthermore, the triangle on the left has angles of x, 180- y, and 60, which is angle TRS.

Using our first equation, we have:

20 + 60 + 180 - y = 180

y = 80

Answer: D
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Re: In the equilateral triangle RST above, y equals   [#permalink] 29 Aug 2017, 17:24
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