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Question
In the given figure, AB || DE. Find ∠ACD.
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Solution
In the given problem, AB || DE
We need to find ∠ACD
Now, AB || DE and AEis the transversal, so using the property, “alternate interior angles are equal”, we get,
∠BAE = ∠AED
∠AED = 30
Further, applying angle sum property of the triangle
In ΔDCE
∠DCE + ∠D + ∠E = 180
∠DCE + 40 + 30 = 180
∠DCE + 70 = 180
∠DCE = 180° - 70°
∠DCE = 110°
Further, ACE is a straight line, so using the property, “the angles forming a linear pair are supplementary”, we get,
∠ACD + ∠DCE = 180°
∠ACD + 110 = 180°
∠ACD = 180 - 110°
∠ACD = 70°
Therefore, ∠ACD = 70° .
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