In the given figure, AB || CD, ∠BAE = 65° and ∠OEC = 20°. Find ∠ECO.

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Solution

In the given figure, AB || CD and AE is the transversal.

∴ ∠DOE = ∠BAE (Pair of corresponding angles)

⇒ ∠DOE = 65°

In ∆COE,

∠DOE = ∠OEC + ∠ECO (Exterior angle of a triangle is equal to the sum of two opposite interior angles)

⇒ 65° = 20° + ∠ECO

⇒ ∠ECO = 65° − 20° = 45°

Thus, the measure of ∠ECO is 45°.

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$In the given figure , A B | | C D, ∠ B A E = 65^{\circ} a n d ∠ O E C = 20^{\circ} . F i n d ∠ E C O .$

A B | | C D, ∠ B A E = 45^{\circ}, ∠ D C E = 50^{\circ}

∠ C E D = x

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