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Question

# In the figure above, ¯¯¯¯¯¯¯¯AB,¯¯¯¯¯¯¯¯¯CD and ¯¯¯¯¯¯¯¯EF intersect at P.If r=90o,s=50o,t=60o,u=45o and w=50o, what is the value of x ?

A
45o
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B
50o
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C
65o
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D
75o
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E
It cannot be determined from the information given
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Solution

## The correct option is C 65oFrom the given figure,Sum of the angles in a △PBF = 180∠BPF + s + t = 180Given that s = 50 and t = 60,∠BPF + 50 + 60 = 180∠BPF = 180 − 110∠BPF = 70Sum of the angles in a △PAD = 180∠APD + w + u = 180Given that w = 50 and u = 45,∠APD + 50 + 45 = 180∠APD = 180 − 95∠APD = 85Sum of the angles in a straight line = 180∠BPF + ∠APD + ∠DPF = 18070 + 85 + ∠DPF = 180∠DPF = 180 − 155∠DPF = 25Vertically opposite angles are equal.Here, ∠DPF and ∠EPC are vertically opposite angles.∠DPF = ∠EPC = 25Sum of the angles in a △EPC = 180∠EPC + r + x = 180Given that r = 90,25 + 90 + x = 180x = 180 − 115x = 65Therefore, the value of ′x′ is ′65′.

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