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Question

In the figure, AC || DF.
CBO=40 and FEO=30
What is the value of the reflex angle BOE?

A
290
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B
70
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C
105
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D
45
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Solution

The correct option is A 290
To find the reflex BOE, we first need to find the convex BOE.

To find the convex BOE, we draw a line PQ which is parallel to AC and DF passing through O.


Now, POE=OEF (Alternate interior angles)

POE=30 ----------- (1)

And, BOP=OBC (Alternate interior angles)

BOP=40 ----------- (2)

From (1) and (2),
BOE=BOP+POE=40+30=70

Thus, the convex angle BOE is equal to 70

Now, reflex angle BOE = 36070=290

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