Question

In the fig, $\square PQRS$ and $\square ABCR$ are two parallelograms.
If $\angle P={110}^o$ then find the measures of all angles of $\square ABCR$.

Answer 1

Given:- $PQRS$ and $ABCR$ are parallelograme

$\angle P={110}^0$

$\Rightarrow \angle SRQ={110}^0$ (opposite angle of a parallelogram. are equal).

$\Rightarrow \angle ARC={110}^0$

if $\angle =ARC={110}^0$

$\Rightarrow \angle ABC={110}^0$ (opposite of angle of $\angle ARC$ of parallelogram $ABCR$)

Sum of adjunct angles of a parallelogram $={180}^0$

$\angle ABC+\angle BCR={180}^0$ ......(1)

$\angle ABC+\angle BAR={180}^0$ ......(2)

$\angle BCR=180-\angle ABC=180-110={70}^0$

$\angle BAR=180-\angle ABC=180-110={70}^0$

$\therefore$ in parallelogram $ABCR$

$\angle A={70}^0,\angle B={110}^0,\angle C={70}^0,\angle R={110}^0$