Question

Given circle QQ with radii start overline, Q, S, end overline QS ​ , start overline, Q, R, end overline QR ​ , and start overline, Q, T, end overline QT ​ and chords start overline, U, S, end overline US and start overline, R, T, end overline RT , start overline, U, S, end overline, \parallel, start overline, R, T, end overline US ∥ RT . Name an angle that has the same measure as angle, Q, S, U∠QSU.

Answer 1

An angle that has the same measure as angle ORQ in the circle given is: ∠OQR.

What are radii of a circle?

The radii of a circle are straight line segments that connect the center of the circle to any point on its circumference, and they are all equal in measure.

In the circle given, OQ and OR are radii, which means they have equal measure. Therefore, triangle ORQ is an isosceles triangle because it has two equal sides (OQ = OR).

Based on this, the base angles, ∠ORQ and ∠OQR are congruent to each other.

Thus, a named angle that is equal to ∠ORQ is ∠OQR.

Complete Question:

Given circle O with radii OQ, OP, and OR and chords PR and QR. Name an angle that has the same measure as ∠ORQ.