Question

In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5𝒙 - 7 and CD = 3𝒙 + 1; find the length of CD.


[4 marks]

Answer 1

Let ∠B = 𝒚

Then, ∠A = 3∠B = 3𝒚

Since AD∣∣BC

∴ ∠A + ∠B = 180° (Adjacent angles are supplementary)

⇒ 3𝒚 + 𝒚 = 180°
⇒ 4𝒚 = 180°
⇒ 𝒚 = 45°

Thus, ∠B = 45°

and ∠A = 3𝒚 = 3 × 45 = 135°
[1.5 marks]

Opposite angles of parallelogram are equal,

∴ ∠B = ∠D = 45° and ∠A = ∠C = 135°
[0.5 mark]

Opposite sides of parallelogram are equal, i.e. AB = CD

∴ 5𝒙 − 7 = 3𝒙 + 1
⇒5𝒙 − 3𝒙 = 1 + 7
⇒ 2𝒙 = 8
⇒ 𝒙 = 4

CD = (3 × 4) + 1 = 13
[2 marks]