Question

An exterior angle of a parallelogram is 100°. Find all the interior angles of the parallelogram.​

Answer 1

Answer:

The sum of the exterior angle and the corresponding interior angle = 180°

So the corresponding int.angle = 180–110 =70.

But opposite interior angles are equal.

So the measure of the interior and exterior opposite to this angle =70°

Adjacent angles of a parallelogram are supplementary. So the measure of other two angles are 110°,110° (180–70)

Answer 2

ext. angle is 100°

therefore int. angle = 180°-100°= 80° (linear pair)

as we know opp. angles are equal in parallelogram.

therefore there is two 80° angles

as interior angles of parallelogram add up to 360°

therefore 80° +80°+ X+ Y = 360°

hence X+y = 200°

as opp. angles are equal in parallelogram X=y

then 2x = 200°

X= 200°/2= 100° = y

hence interior angles in this parallelogram are 100°+ 100°+ 80°+ 80° = 360°