Question

17) ABCD is a parallelogram. E is a point on AB. Find the values of x,y and z. A B В لما لا 125 xo 56 9 y D C​

Answer 1

Answer:

∠x = 55 ,∠y = 69 ,∠z = 111

Step-by-step explanation:   ∠A = ∠C (opposite angles of a parallelogram are equal) --------------------1️⃣

∠C = y + 56

hence,  ∠A = y + 56  

In triangle  ΔEBC

∠BEC + x + 56 = 180 (interioir angle sum property of triangle)

∠BEC + z = 180 (linear pair)

∠C + ∠B = 180 (sum of angles on the same side of transversal is 180)

125 + ∠B = 180  [∠c = 125 (from 1️⃣)]

therefore, ∠B = 55

∠B = ∠x = 55° (from figure) --------------- 2️⃣

In triangle  ΔEBC

∠x + 56 = ∠z (exterior angle sum property of triangle)

55 + 56 = ∠z (from 2️⃣)  c         jhygvgvhhh))

∠z = 111

∠y = ∠A - 56

     =  125 - 56

     = 69