Question

The measure of one angle of a parallelogram is ${70}^{\circ }$. What are the measure of the remaining angles.​

Answer 1

Given: Measure of one angle of parallelogram is ${70}^{\circ }$.

Let $ABCD$ is a parallelogram with $\angle A={70}^{\circ }$

We know that,
Sum of any two adjacent angles of parallelogram is ${180}^{\circ }$
Opposite angles of parallelogram are equal
$\Rightarrow \angle C=\angle A={70}^{\circ }$

Also, $\angle A+\angle B={180}^{\circ }$
$\Rightarrow {70}^{\circ }+\angle B={180}^{\circ }$
$\Rightarrow \angle B={110}^{\circ }$

$\Rightarrow \angle B=\angle D={110}^{\circ }$

Thus, $\angle B={110}^{\circ },\angle C={70}^{\circ }\text{and}\angle D={110}^{\circ }$

Therefore, the measure of the remaining angles are ${110}^{\circ },{70}^{\circ }\text{and}{110}^{\circ }$