Question

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

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Answer 1

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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Answer 2

Answer:

Therefore, the measure of ∠ROS is 155°.

Step-by-step explanation:

Given:-

∠RPS = 25°

To Find:-

∠ROS

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,

= ∠ORP+∠ROS+∠RPS+∠OSP=360∘

= 90∘ + ∠ros + 25∘ + 90∘ = 360∘

= 205∘ + ∠ros = 360∘

= ∠ros = 360∘ - 205∘

= ∠ros = ∠ROS=155∘

Therefore, the measure of ∠ROS is 155°.