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$P Q$ is a chord of a circle and $P T$ is a tangent. The measure of $∠ Q P T = 60 °$ then $∠ P R Q$ =[[1]].

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Detailed Solution

P Q

is a chord of a circle and

P T

is a tangent. The measure of

∠ Q P T = 60 °

then

∠ P R Q

120 °

.
Given,

∠ Q P T = 60 °

Considering the tangent

P T

, Sum of angles on either side of a line is

180 °

∠ A P Q + ∠ Q P T = 180 ° ∠ A P Q + 60 ° = 180 ° ∠ A P Q = 180 ° − 60 ° ∠ A P Q = 120 °

Using the theorem,
The angle formed by a tangent and a chord at the point of contact and the angle in the alternate segment are equal. Therefore we get,

∠ A P Q = ∠ P R Q ∠ A P Q = 120 °

Thus, the measure of

∠ P R Q = 120 °

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