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In the diagram, O is the center of the circle. PQ and RS are tangents to the circle. The angle between the two tangents is given as m=80 degrees. Find the angle n at the center subtended by the points

Mathematics

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Question 43:
In the diagram, OO is the center of the circle. PQPQ and RSRS are tangents to the circle.
The angle between the two tangents is given as m∘=80∘m^\circ = 80^\circ.
The angle at the center subtended by the points of tangency is n∘n^\circ.
A property of circles states that the angle between two tangents drawn from an external point to a circle and the angle subtended by the line segment joining the points of contact at the center are supplementary.
Therefore, m∘+n∘=180∘m^\circ + n^\circ = 180^\circ.
Given m∘=80∘m^\circ = 80^\circ, we can find $n^\circ

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