Question

If ∠A and ∠C are two opposite angles of a parallelogram, then:​

Answer 1

Answer:

Angle A = angle C

Step-by-step explanation:

The opposite angles of a parallelogram are equal (and conversely: if the opposite angles of a quadrilateral are equal, it is a parallelogram). The diagonals of a parallelogram bisect each other (and conversely: if the diagonals of a quadrilateral bisect each other, it is a parallelogram).

Answer 2

Step-by-step explanation:

Given:

$ABCD$ is a parallelogram.

To find: Relation between ∠$A$ and ∠$C$.

Calculation:

A parallelogram has opposite sides parallel to each other.

A parallelogram has opposite sides equal to each other.

In the figure below,

$AB||DC\\AD||BC$

From interior angles property of parallel lines, ∠$A+$∠$B=180^{o}$

So, ∠$B+$∠$C=180^{o}$

Therefore, ∠$A=$∠$C$.

Hence, opposite angles are equal in a parallelogram.

Answer:

∠$A=$∠$C$