# Prove that each angle of rectangle measures 90 degree

We know that a rectangle is basically a parallelogram with one angle measures 90 degree.

Given:
Since all rectangle are form of parallelogram, their opposite sides are parallel.
AB || CD and AD || CB.

Also one of the angle measures 90 degree.
∠A = 90 degree

To Prove:
Each angle of rectangle measures 90 degree.
∠A = ∠B = ∠C = ∠D = 90 degree

Proof:
AD & BC are parallel lines intersected by transversal AB.

We know that sum of interior angle on same side of transversal measures 180 degree.

∠A +∠B = 180

90 + ∠B = 180

∠B = 180 – 90

∠B = 90 degree

Similarly line AB & CD are parallel lines intersected by transversal CB.

Here ∠B & ∠C are interior angle on same side.
∠B + ∠C = 180

90 + ∠C = 180

∠C = 90 degree

Similarly line CB & AD are parallel lines intersected by transversal CD.

Here ∠D & ∠C are interior angle on same side.

Similarly line AB & CD are parallel lines intersected by transversal CB.

Here ∠B & ∠C are interior angle on same side.
∠C + ∠D = 180

90 + ∠D = 180

∠D = 90 degree

On combining all the result we get all the angle measure 90 degree.
∠A = ∠B = ∠C = ∠D =90 degree

Hence in rectangle all the angles are right angles.