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1. The measure of arc YX is 56 degrees. Find the measure of angle STY.

62 degrees

56 degrees

90 degrees

112 degrees

1 The measure of arc YX is 56 degrees Find the measure of angle STY 62 degrees 56 degrees 90 degrees 112 degrees

Answer :

Central angle STY matches intercepted arc YX, so its measure is the same: 56 degrees.

Certainly, I can help you with this.

Identify the central angle and its intercepted arc

Since the question asks for the measure of angle STY, and S and T are both on the circumference of the circle, STY must be a central angle.

In the diagram, we also see that arc YX is intercepted by angle STY.

Apply the central angle theorem

The central angle theorem states that the measure of a central angle is equal to the measure of the intercepted arc.

Therefore, in this case, the measure of angle STY is equal to the measure of arc YX, which is given as 56 degrees.

The measure of angle STY is 56 degrees.

Therefore, the correct answer is 56 degrees.

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