Question

In the given figure, AB || DE. Find ∠ACD.

Answer 1

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° .