Bunuel wrote:
In ∆ ABC above, what is the sum of p + q + r + s + t + u ?
(A) 180
(B) 225
(C) 270
(D) 360
(E) 450
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A, B, and C are interior angles of the larger ∆ ABC
So A + B + C = 180(A + B + C) can be used to find p + q + r + s + t + u
Angles in each small triangle (yellow, purple, green) also sum to 180.
From diagram, write the equations -- and add them
r + s + A = 180
p + q + B = 180
t + u + C = 180____________________
r + s +
A + p + q +
B + t + u +
C = 540, or
p + q + r + s + t + u +
(A + B + C) = 540, or
p + q + r + s + t + u +
180 = 540
p + q + r + s + t + u = 360
Answer D
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