Question

in the parallelogram ABCD angle A is equal Angle B + 50 degree then find the measure of each angle of a quadrilateral ABCD​

Answer 1

The value of $\angle A,\angle B,\angle C\ and\ \angle D$ are $115\ degree,65\ degree,115\ degree\ and\ 65\ degree$

Step-by-step explanation:

Given,

In parallelogram $ABCD$ and $\angle A=\angle B+50$

We know,

In  parallelogram opposite angle are equal.

So, From diagram,

$\angle A$ and $\angle C$ are equal and $\angle B$ and $\angle D$ are equal.

Also we know,

Sum of all angle in any quadrilateral equal $360\ degree$.

So,

$\angle A+\angle B+\angle C+\angle D=360$

⇒$2\angle A+2\angle B=360$

⇒$2(\angle B+50)+2\angle B=360$ (∵ $\angle A=\angle B+50$ )

⇒$2\angle B+100+2\angle B=360$

⇒$4\angle B=260$

⇒$\angle B=\frac{260}{4}$

∴ $\angle B=65\ degree$

∴$\angle B=\angle D=65\ degree$

And, $\angle A=\angle C=(65+50)=115\ degree$

Hence, The value of $\angle A,\angle B,\angle C\ and\ \angle D$ are $115\ degree,65\ degree,115\ degree\ and\ 65\ degree$