Question

If one angle of a parallelogram is ${65}^{\circ },$ find the measure of other angles.

Answer 1

As we know,

Opposite angles of a parallelogram are equal.

$⟹\angle A=\angle C={65}^{\circ }$

and let us say that, $\angle B=\angle D=\theta$

${65}^{\circ }+\theta +{65}^{\circ }+\theta ={360}^{\circ }2\theta +{130}^{\circ }={360}^{\circ }2\theta ={230}^{\circ }\therefore \theta =\left(\frac{{230}^{\circ }}{2}\right)={115}^{\circ }$

$\text{So angles are}{65}^{\circ },{65}^{\circ },{115}^{\circ }$and${115}^{\circ }$.