The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, ∠A = 60° and vertex C = (7, 5). Find the equations of BC and CD.

Given, ∠A = 60° and vertex C = (7, 5)

As, ABCD is a parallelogram, we have

∠A + ∠B = 180° [Sum of adjacent angles in a || gm = 180°]

∠B = 180° – 60° = 120°

So, the anticlockwise angle of BC from x-axis is (180° - 120°) = 60°.

Slope of BC = tan 60° = $\sqrt{3}$

By point-slope form,

Equation of line BC is :

⇒ y – y₁ = m(x – x₁)

⇒ y – 5 = $\sqrt{3}$(x – 7)

⇒ y – 5 = $\sqrt{3}x - 7\sqrt{3}$

⇒ y = $\sqrt{3}x - 7\sqrt{3} + 5$

As, CD || AB and AB || x-axis

Slope of CD = Slope of AB = 0 [As slope of x-axis is zero]

By point-slope form,

Equation of line CD is :

⇒ y – y₁ = m(x – x₁)

⇒ y – 5 = 0(x – 7)

⇒ y = 5.

Hence, equation of BC is y = $\sqrt{3}x - 7\sqrt{3} + 5$ and CD is y = 5.