in rectangle pqrs diagonal PR and QS intersect at O if angle rpq is 30 degree find angle r o s​

  • matematika

    Subject:

    Math

  • Author:

    pitts

  • Created:

    1 year ago

Answers 2

In the given rectangle Angle ROS is 105°

answer img

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°.

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