In circle t, ∠PTQ ≅ ∠RTS. What is the measure of arc PQ?

Solution:

Central angle is the angle formed by two arms with the center of a circle as the vertex.

The radius vectors form the arms of the angle.

Here, O is the center of the circle,

AB is the arc

OA is a radius

OB is another radius

Central angle = (s × 360°)/2πr

Where, s is the length of the arc

r is the radius of the circle

From the figure given above, ∠PTQ and ∠RTS are central angle.

T is the center of the circle

We know that,

m arc PQ = m∠PTQ --- (by central angle)

m∠RTS = m arc SR --- (by central angle)

m arc SR = 66°

So, m∠RTS = 66°

Given, m∠PTQ ≅ m∠RTS

So, m∠PTQ = 66°

Therefore, measure of arc PQ = 66°.

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In circle t, ∠PTQ ≅ ∠RTS. What is the measure of arc PQ?

Summary:

In circle t, ∠PTQ ≅ ∠RTS. The measure of arc PQ is 66°.