Question

In a circle, PQ=RS and angle ORS =48 find angle OPQ and angle ROS

Answer 1

I think u understand it

Answer 2

The value of $\angle OPQ$ is $48$° and $\angle ROS$ is $84$°

Step-by-step explanation:

Given,

A circle, $PQ=RS$ and $\angle ORS=48$°

From figure,

In $\triangle ORS$,

$\angle ORS=\angle OSR=48$°  (∵ $OR=OS$ radius of the circle )

∴ $\angle ORS+\angle OSR+\angle ROS=180$

⇒$\angle ROS=180-48-48$

∴ $\angle ROS=84$°

From $\triangle ORS$ and $\triangle ORS$,

• $PQ=RS$ (Given )

• $OR=OQ$ (Radius)

• $OP=OS$ (Radius)

∴ $\triangle ORS$ ≅ $\triangle ORS$

∴ $\angle OPQ=\angle ORS$

∴ $\angle OPQ=48$°

So, The value of $\angle OPQ$ is $48$° and $\angle ROS$ is $84$°