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If from any external point, two tangents are drawn, then find the addition of angles made by the intersection of two tangents and the angle made by the intersection of two radii at the center facing the same external point  

If from any external point, two tangents are drawn, then find the addition of angles made by the intersection of two tangents and the angle made by the intersection of two radii at the center facing the same external point   Correct Answer 180° 

Given:

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Concept Used:

Tangent is always perpendicular to the radius at the point of contact.

Calculation:

⇒ ∠ RPQ = ∠ RQO = 90° 

In □ RPOQ,

The Sum of measures of all angles is 360° 

∠R + ∠P + ∠O + ∠Q = 360° 

⇒ ∠R + ∠O = 360 – (90 + 90)

⇒ ∠R + ∠O = 360 – 180

⇒ ∠R + ∠O = 180° 

∴ The sum of the measure of two angles is 180°   

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