Question

for the triangle shown, triangle abc is dilated by a scale factor of 3 to obtain triangle xyz, where d = 21. what is the measure, in degrees, of angle x? note: figure not drawn to scale a. 20 b. 57 c. 00 d. 63

Explanation:

Step1: Recall dilation property

Dilation preserves angle - measures.

Step2: Identify angle in similar triangles

Since \(\triangle ABC\) is dilated to \(\triangle XYZ\), \(\angle X=\angle A\).
If we assume \(\angle A = 60^{\circ}\) (from the given triangle \(ABC\) where one angle is marked as \(60^{\circ}\)), then \(\angle X = 60^{\circ}\). But it seems there is a mis - match with the options provided. If we assume this is a right - triangle related problem and we use trigonometry (which is not necessary as dilation preserves angles), we note that the angle measure is unchanged by dilation. So the measure of angle \(X\) is the same as the corresponding angle in \(\triangle ABC\). Since the angle in \(\triangle ABC\) is \(60^{\circ}\), the measure of angle \(X\) is \(60^{\circ}\). However, if we assume there is some error and we consider the closest option to \(60^{\circ}\) among the given options.

Answer:

c. 60