Question

If KITE is a parallelogram, then which angle is equivalent to the sum of $\angle A$ and $\angle R$ ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

In $△EAR$ ,

$\angle E$ + $\angle A$ + $\angle R$ = 180° [$\because$ Angle sum property]
$\Rightarrow$ $\angle A$ + $\angle R$ =180° - $\angle E$
$\Rightarrow$ $\angle A$ + $\angle R$ =180° - $\angle KET$
[$\because$ $\angle E$ and $\angle KET$ vertically opposite angles]
Now, $\angle KET$ = 180° - $\angle EKI$ [$\because$ Adjacent agles of a parallelogram are supplementary.]
$\Rightarrow$ $\angle A$ +$\angle R$ =180° - (180° - $\angle EKI$ )
=180° - 180° + $\angle EKI$
$\Rightarrow$ $\angle A$ + $\angle R$ = $\angle EKI$