Question

In the figure, AB⎯⎯⎯⎯⎯ is parallel to DE⎯⎯⎯⎯⎯.Select from the drop-down menu to correctly complete the statement.TriangleABC and triangleDEC are :choices similar or not similar

Answer 1

Solution

In the diagram,

∠DCE = ∠ACB = 60 (vertically opposite angle are equal)

∠ABC = ∠CDE = 72 (alternate angle are equal)

∠BAC + ∠ACB + ∠CBA = 180

=> ∠BAC = 180 - ∠ACB - ∠CBA = 180 - 60 - 72 = 48

Also, ∠CED = ∠BAC = 48

SInce ∠A = ∠D, ∠B = ∠E and ∠C = ∠C

Hence △ABC is similar to △DEC