Question

justify reasoning three students used the figure to write a statement. they want to know who is correct. samar: ∠wzu is a right angle. jana: ∠yzu and ∠uzv are supplementary. antonio: ∠vzu is adjacent to ∠yzx. which of these statements are correct? select all correct answers. figure: horizontal line x-z-u, vertical line z-w (right angle), line y-z-v through z □ samar is correct.

Explanation:

Step1: Analyze Samar's statement

From the figure, \( \angle WZU \) has a right - angle symbol. By the definition of a right angle (an angle with a measure of \( 90^{\circ} \)), \( \angle WZU = 90^{\circ} \), so Samar's statement is correct.

Step2: Analyze Jana's statement

Supplementary angles are two angles whose sum is \( 180^{\circ} \). \( \angle YZU \) and \( \angle UZV \) are adjacent angles that form a linear pair? No, actually, \( \angle YZU \) and \( \angle UZV \) are adjacent and their non - common sides form a straight line? Wait, no. Let's look at the angles. \( \angle YZU \) and \( \angle UZV \): the sum of \( \angle YZU+\angle UZV=\angle YZV \), which is not \( 180^{\circ} \). Wait, maybe I made a mistake. Wait, \( \angle YZU \) and \( \angle UZV \): actually, \( \angle YZU \) and \( \angle UZV \) are adjacent angles, but their sum is not \( 180^{\circ} \). Wait, no, let's re - examine. The angle \( \angle YZU \) and \( \angle UZV \): if we look at the lines, \( YZ \) and \( VZ \) with \( ZU \) as a common side. Wait, maybe the correct way: \( \angle YZU \) and \( \angle UZV \) are adjacent, but their sum is not \( 180^{\circ} \). Wait, but Samar's statement: the right - angle symbol between \( WZ \) and \( ZU \) means \( \angle WZU = 90^{\circ} \), so Samar is correct.

Step3: Analyze Antonio's statement

Adjacent angles share a common side and a common vertex, and their non - common sides are different. \( \angle VZU \) and \( \angle YZX \): \( \angle YZX \) and \( \angle VZU \) are vertical angles? Wait, \( \angle YZX \) and \( \angle VZU \) are vertical angles (since \( XY \) and \( VU \) are intersecting lines), so they are not adjacent. Adjacent angles must share a common side. \( \angle VZU \) and \( \angle YZX \) do not share a common side, so Antonio's statement is incorrect. And for Jana: \( \angle YZU \) and \( \angle UZV \): their sum is not \( 180^{\circ} \), so Jana's statement is incorrect.

Answer:

Samar is correct.