Question

prove that each angles of a rectangle is 90 degree

Answer 1

Given: Rectangle ABCD.

Prove: Angles BAD = 90, CBA = 90, DCB = 90, and ADC = 90.

A rectangle is a parallelogram, so the definition and properties of a parallelogram apply to a rectangle.  Consider how a rectangle is constructed------parallel lines.

The main properties of a rectangle is that it is made up of right angles. Right angle=90 degrees

Answer 2

To ,

Prove that each angles of a rectangle is of 90°.

Solution :-

Let ABCD be a given parallelogram with ∠A = 90°

→ ∠ A = ∠ B = ∠ C = ∠ D = 90°

so,

→ ∠ A + ∠ B = 180° [ Interior angles on same side of a transversal.]

→ $\therefore$ ∠ B = ∠ A -180°

⠀∠ B = 90°-180°

⠀→ ∠ B = 90°

∠ C = ∠ A = 90°

∠ D = ∠ B = 90° [ Opposite angles of the parallelogram.]

So,

∠ C = 90°

∠ D = 90°

$\therefore$ ∠ A = ∠ B = ∠ C = ∠ D = 90°

Hence proved.