Question

If PQRS is a rhombus with angle pqr = 55find angle PRS

Answer 1

Angle PQR + angle QRS = 180
55+qrs=180
qrs=180-55=125
Angle prs= 1/2 angle qrs
(Diagonals of a rhombus bisect opposite angles.)
So angle prs = 62.5

Answer 2

Therefore $\angle PRS$ value is $62.5$ degree.

Step-by-step explanation:

Given;

$PQRS$ is a rhombus and $\angle PQR=55$ degree

For a Rhombus opposite two angle are equal.

∴$\angle PQR=\angle PSR=55$ degree

And $\angle QPS=\angle QRS$

Then,

$2\angle PQR+2\angle QRS=360$

⇒$2\angle QRS=360-2\angle PQR$

⇒$2\angle QRS=360-(2\times 55)$

⇒$2\angle QRS=360-110$

⇒$2\angle QRS=250$

∴ $\angle QRS=125$

∵ Diagonals of a rhombus bisect opposite angles.

So,

$\angle PRS=\frac{1}{2} \angle QRS$

⇒$\angle PRS=\frac{1}{2} \times 125$

∴$\angle PRS=62.5$

∴ $\angle PRS$ value is $62.5$ degree.