Question

Opposite angles of a parallelogram are ____ .

• A. Equal
• B. Supplemantary
• C. Complementary
• D. Unequal

Answer 1

The correct option is A Equal

In the given parallelogram, AD || BC and AB || DC
Consider the diagonal BD which acts as a transversal for BC and AD.
$\angle ADB=\angle DBC=x^{\circ }$ ( alternate angles)

Consider the diagonal BD which acts as a transversal for AB and BC.
$\angle ABD=\angle BDC=y^{\circ }$ ( alternate angles)

We can see that
$\angle B=\angle ABD+\angle DBC=x^{\circ }+y^{\circ }$
Also, $\angle D=\angle ADB+\angle BDC=x^{\circ }+y^{\circ }$
Thus, $\angle B=\angle D$.

Hence, opposite angles of a parallelogram are equal.