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.