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Finding Unknown Angles

In the given ...

Question

In the given figure, CD and FE are parallel lines. Find the value of x.

12^{\circ}

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13^{\circ}

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14^{\circ}

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15^{\circ}

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Solution

The correct option is B $13^{\circ}$

From point O, draw a line OP parallel to CD.
Thus, OP || CD || EF.
∠COP = ∠BCD = 4x [Corresponding angles]
∠EOP = ∠FEA = 6x [Corresponding angles]
Now, ∠COP + ∠EOP = ∠COE
⇒ $6 x + 4 x = 130^{o}$
⇒ $10 x = 130^{o}$
⇒ $x = 13^{o}$

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