Question

In the figure, AB II CD and AC = EC. Find x, y and z.

Answer 1

Answer:

x = 42°

y = 66°

z = 48°

Step-by-step explanation:

AB||CD and AD is the transversal

=> Angle BAD = Angle CDA (Alternate Interior Angles)

=> x = 42°

Now Angle ECD + Angle EDC = Angle CEA (Exterior Angle property of a triangle)

=> Angle CEA = 24+42 = 66°

Now angle CEA = Angle CAE (AC = EC and angles opposite to equal sides in a triangle are equal)

=> y = 66°

Now Angle CEA + Angle CAE + Angle ACE = 180° (Angle Sum Property of a triangle)

=> z+66+66 = 180°

=> z+132° = 180°

=> z = 48°