The value of m∠RTS = 32°, found using the theorem: the angle subtended by an arc at the center of a circle is twice the angle the arc subtends at its circumference. Hence, option 1 is the right choice.
What are the relation between the angle at the center and the angle at the circumference?
The angle subtended by an arc at the center of a circle is twice the angle the arc subtends at its circumference.
How do we solve the given question?
In the figure, we are given the measure of arc RS as 64°. This implies that the arc RS subtends an angle of 64° at the center, that is, m∠ROS = 64°.
By theorem, we know that the angle subtended by an arc at the center of a circle is twice the angle the arc subtends at its circumference.
Since point T is on the circumference of the circle,
m∠RTS = (1/2)*m∠ROS
or, m∠RTS = (1/2) * 64° = 32°.
∴ The value of m∠RTS = 32°, found using the theorem: the angle subtended by an arc at the center of a circle is twice the angle the arc subtends at its circumference. Hence, option 1 is the right choice.
Learn more about the Theorems of Circle at
https://brainly.com/question/26594685
#SPJ2
