Question

julian describes an angle in the triangle using these statements.
\\(\overline{gh}\\) is the adjacent side.
\\(\overline{hk}\\) is the opposite side.
\\(\overline{gk}\\) is the hypotenuse.
which angle(s) is julian describing?
\\(\circ\\) \\(\angle g\\)
\\(\circ\\) \\(\angle h\\)
\\(\circ\\) \\(\angle k\\)
\\(\circ\\) \\(\angle h\\) and \\(\angle k\\)

Explanation:

Step1: Identify right triangle parts

The triangle is right-angled at $H$, so hypotenuse $\overline{GK}$ is correct (hypotenuse is opposite right angle).

Step2: Match sides to angle

For $\angle G$:

• Adjacent side: $\overline{GH}$ (shares vertex $G$ and right angle $H$)
• Opposite side: $\overline{HK}$ (does not share vertex $G$)
• Hypotenuse: $\overline{GK}$ (matches given statement)

Step3: Verify other angles

For $\angle H$: It is the right angle, so it has no "opposite/adjacent" in this context.
For $\angle K$: Adjacent side would be $\overline{HK}$, opposite would be $\overline{GH}$, which does not match the given statements.

Answer:

$\boldsymbol{\angle G}$