Question

use the image to answer the question. isha constructed ∠xyz and needs to double the angle by constructing a copy of the angle using ray yx as one of the sides of the new angle. he has constructed an arc, as appears in the image. what next step must he take to construct a copy of the angle using ray yx? (1 point) he must measure the distance between point x and point z using a compass. he must draw an arc that intersects the larger arc by placing the pointed end on point x. he must measure the distance between point y and point z using a compass. he must measure the distance between point y and the arc using a compass.

Explanation:

To construct a copy of an angle with one side as ray \(YX\), we use the property of congruent - arcs in angle - construction. First, we measure the distance between the intersection points of the arc with the two sides of the original angle. In this case, the intersection points are \(X\) and \(Z\) of the arc with the sides of \(\angle XYZ\). Measuring this distance with a compass and then using it to mark a new point on the new arc (constructed with the same radius from point \(X\)) helps in creating a congruent angle.

Answer:

He must measure the distance between point \(X\) and point \(Z\) using a compass.