Question

looking at ∠x, identify the red side as the hypotenuse, adjacent, or opposite
none of the above
opposite
hypotenuse

Explanation:

Step1: Recall triangle side definitions

In a right - triangle, the hypotenuse is the side opposite the right angle (the longest side). The adjacent side to an angle is the non - hypotenuse side that forms the angle with the hypotenuse. The opposite side is the side that does not form the angle and is opposite to the angle.

In right - triangle \(XYZ\) with right angle at \(Y\), we are looking at \(\angle X\). The red side is \(XZ\).

Step2: Identify the type of side

The right angle is at \(Y\), so the hypotenuse is the side opposite \(\angle Y\), which is \(XZ\) (the red side). The adjacent side to \(\angle X\) would be \(XY\) (since it forms \(\angle X\) with the hypotenuse \(XZ\)) and the opposite side would be \(YZ\) (opposite to \(\angle X\)). Since \(XZ\) is opposite the right angle, it is the hypotenuse.

Answer:

The red side ( \(XZ\)) is the hypotenuse. So the answer is the option corresponding to "Hypotenuse" (the green - colored option with "Hypotenuse" text in the given options).