Question

which one doesnt belong three students used the figure to write a statement. is each statement correct? justify your conclusion.
samar: ∠wzu is a right angle.
jana: ∠yzu and ∠uzv are supplementary.
antonio: ∠vzu is adjacent to ∠yzx.

Explanation:

Step1: Analyze Samar's statement

A right - angle is an angle of \(90^{\circ}\). From the figure, \(\angle WZU\) is marked as a right - angle. So, Samar's statement \(\angle WZU\) is a right angle is correct.

Step2: Analyze Jana's statement

Two angles are supplementary if their sum is \(180^{\circ}\). \(\angle YZU\) and \(\angle UZV\) form a linear pair (they lie on a straight line). By the linear - pair postulate, \(\angle YZU+\angle UZV = 180^{\circ}\). So, Jana's statement \(\angle YZU\) and \(\angle UZV\) are supplementary is correct.

Step3: Analyze Antonio's statement

Adjacent angles must have a common vertex, a common side, and no overlapping interior points. \(\angle VZU\) and \(\angle YZX\) have a common vertex \(Z\), but they do not have a common side. So, Antonio's statement \(\angle VZU\) is adjacent to \(\angle YZX\) is incorrect.

Answer:

Antonio's statement doesn't belong. Samar's statement is correct as \(\angle WZU\) is marked as a right - angle. Jana's statement is correct since \(\angle YZU\) and \(\angle UZV\) form a linear pair (\(\angle YZU+\angle UZV=180^{\circ}\)). Antonio's statement is incorrect because \(\angle VZU\) and \(\angle YZX\) do not have a common side (a requirement for adjacent angles).