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Bunuel
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In triangle, DCE, angle DCE = 180 - (90 + 40)
=180 - 130 = 50

In triangle ABC, which is isosceles
angle BAC = angle BCA = 45

Now angle BCA + BCD + DCE = 180
45 + x + 50 = 180
x = 85

IMO E
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Bunuel
In the figure below, what is the value of x?


A. 45
B. 50
C. 65
D. 70
E. 85

Concept: External Angle = Sum of Opposite internal angles.

Hence, <ACD = <CDE + <CED = 40 + 90 ---------(1)
Also ABC is right issoseless triangle, So <BCA = 45.------------(2)

We know that <ACD = <BCA+x
Using (1) & (2) we can derive 40+90 = 45+x, So x=85

IMO E
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