Question

explore polygons that can be created by radii and chords by following these steps. 1. move point x to point b and point z to point a and observe the inscribed polygon. note that xz is a diameter of the circle. the polygon inscribed in the circle is a triangle. 2. move point y and observe what happens to the measure of angle xyz. angle xyz is always dropdown with an acute, a right, an obtuse angle. m∠xyz = 90° (with a circle diagram having points x, y, z and center o)

Explanation:

By the Thales' theorem (or inscribed angle theorem), an angle inscribed in a semicircle is a right angle. Here, \( XZ \) is the diameter (so it forms a semicircle), and \( \angle XYZ \) is an inscribed angle subtended by the diameter. So regardless of where point \( Y \) is on the circle (as long as it's not on \( XZ \) itself), \( \angle XYZ \) will always be a right angle.

Answer:

a right