Given:
Angle RPQ=30°
To find:
The angle ROS
Solution:
The angle ROS=120°.
We know that the rectangle's diagonals are having an equal length and they also divide each other into two equal halves.
So, OP=OR and OQ=OS.
Also, OP=OQ and OR=OS.
Now, in ΔPOQ,
Angle SQP=angle RPQ (corresponding to equal sides OP and OQ)
So, angle SQP=30°
Angle SQP+angle RPQ+angle POQ=180°
Using values,
30°+30°+angle POQ=180°
60°+angle POQ =180°
angle POQ=180°-60°
angle POQ=120°
Now, lines PQ and RS are parallel and PR, QS intersect at O.
So, angle POQ=angle ROS (one another's vertically opposite angle)
Angle ROS=120°
Therefore, the angle ROS=120°.