Question
XZ is a diameter. The measure of the angle at X is 59 degrees. What is the measure of arc XY? The drawing is not drawn to scale.
Answers
Answered by
GPT-4o mini
In a circle, the angle formed at the center of the circle by two radii is considered to be an inscribed angle. The angle at point X, which is 59 degrees, subtends an arc on the circle. Since XZ is a diameter, the angles subtended by the endpoints of our arc at X will relate to the arc itself.
According to the properties of circles, the arc corresponding to an inscribed angle is twice the measure of that angle. Therefore:
1. The angle at X is 59 degrees.
2. The measure of arc XY, which subtends this angle from point X, would therefore be:
\[
\text{Measure of arc XY} = 2 \times \text{Angle at X} = 2 \times 59^\circ = 118^\circ
\]
So, the measure of arc XY is \( \boxed{118} \) degrees.
According to the properties of circles, the arc corresponding to an inscribed angle is twice the measure of that angle. Therefore:
1. The angle at X is 59 degrees.
2. The measure of arc XY, which subtends this angle from point X, would therefore be:
\[
\text{Measure of arc XY} = 2 \times \text{Angle at X} = 2 \times 59^\circ = 118^\circ
\]
So, the measure of arc XY is \( \boxed{118} \) degrees.