Question

Measure of one angle of a rhombus is ${50}^{\circ }$ .Find the measures of remaining the angles.

Answer 1

Suppose there is a rhombus $ABCD$ having angles $\angle A,\angle B,\angle C,\angle D$ as shown in figure and $\angle A={50}^{\circ }\left(given\right)$

As we know that in a rhombus, two adjacent angles are supplementary then

$\angle A+\angle C={180}^{\circ }$,

${50}^{\circ }+\angle C={180}^{\circ }$,

$\angle C={130}^{\circ }.$

Also, $\angle A=\angle D={50}^{\circ }$ and $\angle C=\angle B={130}^{\circ }.$

So the angles of the rhombus having one angle ${50}^{\circ }$ will have remaining angles such as ${130}^{\circ },{50}^{\circ },{130}^{\circ }.$