Question

In the given figure, if ABCD is a parallelogram then find the value of x, y and z (in degrees).

(4 marks)

Answer 1

Since, ABCD is a parallelogram,

∠A + ∠D = 180° (Adjacent angles of a parallelogram are supplementary).

⇒ 125° + x = 180°
⇒ x = 180° – 125°
⇒ x = 55°

(1.5 marks)

Also, ∠A = ∠C (Opposite angles of a parallelogram are equal)

⇒ 125° = y + 56°
⇒ y = 125° – 56°
⇒ y = 69°

(1 mark)

Also, if x = 55° then ∠B = 55⁰

Now, in △ECB,
∠B + ∠ECB + ∠BEC = 180⁰ (Angle sum property of a triangle)
⇒ ∠BEC = 180° - (55° + 56°)
⇒ ∠BEC = 59°

Also, ∠BEC + ∠CEA = 180° (Linear pair)
⇒ 59⁰ + z = 180°
⇒ z = 180° - 59°
⇒ z = 111°

(1 mark)

Therefore, the value of x = 55°, y = 69° and z = 111°

(0.5 mark)