Question

In a Parallelogram, show that any two adjacent angles are supplymentry.

《《《《《Please Answer.》》》​》》

Answer 1

Step-by-step explanation:

Given:

• A parallelogram ABCD.

To Show:

• Adjacent angles of ||gm are supplementary.

Proof: In parallelogram ABCD we have

• AB || CD and BC || AD {opposite sides are parallel}

[ Supplementary angles :- Two angles whose sum is equal to 180° ]

Here ,

AB || CD and AD is a transversal.

As we know that interior angles on the same side of a transversal are supplementary. (We can also say that these angles are co - interior angles & sum of co - interior angles is 180°)

Therefore,

∠A + ∠D = 180°

Similarly we can get

∠B + ∠C = 180°

∠C + ∠D = 180°

∠A + ∠B = 180°

Hence, sum of any two adjacent angles of a parallelogram is equal to 180° or supplementary.

• Opposite sides of a ||gm are parallel and equal.
• Area of ||gm = Base × Height
• Perimeter = Sum of all sides.