Question

In the given figure if angle RPS=25 The value of angle ROS is

Answer 1

Given:

∠RPS = 25°

To find:

The value of angle ROS

Solution:

To solve the given problem we will use the following theorem:

The tangent and the radius of a circle makes 90° with each other at the point of contact of the tangent.

Based on the above theorem, we have,

∠PRO = ∠PSO = 90° ..... (i)

From the figure, we can say,

→ PROS is a quadrilateral

So, according to the angle sum property of a quadrilateral, we get

$\angle PRO + \angle ROS + \angle PSO + \angle RPS = 360\°$

substituting the values from (i) and ∠RPS = 25°, we get

$\implies 90\° + \angle ROS + 90\° + 25\° = 360\°$

$\implies \angle ROS + 205\° = 360\°$

$\implies \angle ROS = 360\° - 205\°$

$\implies \bold{\angle ROS = 155\°}$

Thus, the value of → ∠ROS = 155°.

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