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