Question

Two opposite angles of a parallelogram are ${100}^o$ each. Find each of the other two opposite angles.

Answer 1

Given two opposite angles of a parallelogram are ${100}^0$ each

$\because$ Adjacent angles of a parallelogram are supplementary.

$\begin{array}{c}\therefore \angle A+\angle B={180}^0\\ \Rightarrow {100}^0+\angle B={180}^0\\ \Rightarrow \angle B={180}^0-{100}^0\end{array}$

$\Rightarrow \angle B={80}^0$

Also,

Opposite angles of parallelogram are equal

$\begin{array}{c}\therefore \angle D=\angle B={80}^0\\ \therefore \angle B=\angle D={80}^0\end{array}$