Question

In parallelogram ABCD, $\angle D={115}^o$, determine the measure of $\angle A$ and $\angle B$.

Answer 1

Since the sum of any two consecutive angles of a parallelogram is ${180}^o$. Therefore,

$\angle A+\angle D={180}^o$ and $\angle A+\angle B={180}^o$

Now, $\angle A+\angle D={180}^o$

$\angle A+{115}^o={180}^o$

$\angle A={65}^o$

and, $\angle A+\angle B={180}^o$

${65}^o+\angle B={180}^o$

$\angle B={115}^o$

Thus, $\angle A={65}^o$ and $\angle B={115}^o$.