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In the equilateral triangle RST above, y equals
(A) 60
(B) 70
(C) 75
(D) 80
(E) 85
Attachment:
2017-08-25_1040.png [ 8.6 KiB | Viewed 6969 times ]
Luckisnoexcuse
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25 Aug 2017, 00:28
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Bunuel
In the equilateral triangle RST above, y equals
(A) 60
(B) 70
(C) 75
(D) 80
(E) 85
Attachment:
2017-08-25_1040.png
y= x+angleSRT = 20+60 = 80
D
25 Aug 2017, 11:32
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Bunuel
In the equilateral triangle RST above, y equals
(A) 60
(B) 70
(C) 75
(D) 80
(E) 85
Attachment:
2017-08-25_1040.png
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
