Question

In the given figure, if angle RPS = 25°, find the value of angle ROS.. Single line text

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Answer 1

Answer:

155°

Step-by-step explanation:

in given figure,

I is the centre of the circle and R and S are tangent points ,

therefore,<ORP = < OSP = 90°,

therefore ,from quadrilateral ORPS,

<ROS + 90° + 90° + 25° = 360°.

=> <ROS = 360° - 205°,

=> <ROS = 155°.

Hope it helps u...

Answer 2

Given:-

• ∠RPS = 25°

To Find:-

∠ROS

Let us recall:-

Before solving this question we first need to recall the theorems of tangents of a circle.

For this question we need to recall the theorem:-

Angle between the radius of a circle and the tangent is always 90° [Let us assume this theorem to be theorem no. 1]

Solution:-

Now,

∠RPS = 25°

In the figure we can clearly see that,

• PR and PS are the tangent of the circle.
• OR and OS are the radius of the circle.

According to Theorem No.1

∠ORP = 90°

∠OSP = 90°

Now,

A quadrilateral ORPS can be seen.

According to angle sum property of a quadrilateral,

$\sf{\angle ORP + \angle ROS + \angle RPS + \angle OSP = 360^\circ}$

= $\sf{90^\circ + \angle ROS + 25^\circ + 90^\circ = 360^\circ}$

= $\sf{205^\circ + \angle ROS = 360^\circ}$

$\sf{\implies \angle ROS = 360^\circ - 205^\circ}$

= $\sf{\implies \angle ROS = 155^\circ}$

Therefore, the measure of ∠ROS is 155°.

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$\bf{\underline{\large{More!!!}}}$

→ What is angle-sum property of quadrilateral?

✓ Angle-sum property of a quadrilateral states that the sum of all angles of a quadrilateral is always 360°.

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$\bf{\underline{\large{Additional\:Information!!!}}}$

More theorems related to circles:-

• The tangent at any point of a circle is perpendicular to the radius through the points of contact.
• The lengths of tangents drawn from an external point to a circle are equal.

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