Question
Find the remaining angles in the following quadrilaterals.
✓
Answer
Here $P R \| E A$, and $P E \| R A$
Therefore, PEAR is a parallelogram.
$\angle P =\angle A =40^{\circ}$ $\qquad$ (Opposite angles of a parallelogram are equal)
$\angle P +\angle R =180^{\circ}$ $\qquad$ (The sum of the adjacent angles of a parallelogram is $180^{\circ}$ )
$\begin{array}{l}40^{\circ}+\angle R=180^{\circ} \\\angle R=180^{\circ}-40^{\circ} \\\angle R=140^{\circ} . \\\angle R=\angle E=140^{\circ} .\end{array}$$\qquad$ (Opposite angles of a parallelogram are equal)
Therefore, PEAR is a parallelogram.
$\angle P =\angle A =40^{\circ}$ $\qquad$ (Opposite angles of a parallelogram are equal)
$\angle P +\angle R =180^{\circ}$ $\qquad$ (The sum of the adjacent angles of a parallelogram is $180^{\circ}$ )
$\begin{array}{l}40^{\circ}+\angle R=180^{\circ} \\\angle R=180^{\circ}-40^{\circ} \\\angle R=140^{\circ} . \\\angle R=\angle E=140^{\circ} .\end{array}$$\qquad$ (Opposite angles of a parallelogram are equal)
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