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06 Sep 2017, 04:40
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
88% (01:20) correct
12%
(01:23)
wrong
based on 63
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In ∆ ABC above, what is the sum of p + q + r + s + t + u ?
(A) 180
(B) 225
(C) 270
(D) 360
(E) 450
Attachment:
2017-09-06_1535_002.png [ 11.77 KiB | Viewed 2066 times ]
06 Sep 2017, 04:49
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Find : p + q + r + s + t + u
Let the angles of center triangle formed inside big triangle be x, y and z
=> x+y+z=180
Now as Sum of angles on 1 side of straight line = 180
=> p+u+x=180
=>q+r+y=180
=>s+t+z=180
adding all 3.. p+q+r+s+t+u+(x+y+z)= 540
p+q+r+s+t+u = 540 -(x+y+z) = 540-180 =360
Answer: D
Let the angles of center triangle formed inside big triangle be x, y and z
=> x+y+z=180
Now as Sum of angles on 1 side of straight line = 180
=> p+u+x=180
=>q+r+y=180
=>s+t+z=180
adding all 3.. p+q+r+s+t+u+(x+y+z)= 540
p+q+r+s+t+u = 540 -(x+y+z) = 540-180 =360
Answer: D
06 Sep 2017, 05:32
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Attachment:
2017-09-06_1535_002.png [ 12.87 KiB | Viewed 1743 times ]
There are 3 smaller triangles(∆ADE,∆BDF and ∆CEF) each which has a third angle(unmarked) - A,B and C
A + B + C = 180 degree(sum of the three angles of the triangle ABC total 180)
Similarly each of the smaller triangles also has a sum of angles equal to 180.
p + q + r + s + t + u + A + B + C = 540
p + q + r + s + t + u = 540 - 180 = 360(Option D)
