Question

If m angle HGI = 82 degrees, what is m HK?

Answer 1

I don’t have enough information to answer—there’s no diagram or description of where point K is or how H, G, I, K are related. Could you either

- upload the figure, or
- paste the exact problem text, or
- describe the figure (which points are on a circle, which lines are parallel, which angles are given as vertical/adjacent/inscribed/central, etc.)?

If you prefer, here are common interpretations and how to get m∠HK in each case so you can tell me which fits:

- If ∠HGI = 82° is an inscribed angle in a circle and it intercepts arc HI, then arc HI = 2·82° = 164°. If K denotes an endpoint of that arc, you can use that to find arc HK accordingly.
- If ∠HGI is a central angle, then arc HI = 82° (central = arc measure).
- If ∠HGI is an exterior angle of triangle HGI, then m∠HGI = m∠H + m∠I; use any given interior angles to solve for m∠HK if HK refers to one of them.
- If HK is a straight line forming a linear pair with ∠HGI, then m∠HK = 180° − 82° = 98°.
- If ∠HGI and ∠HKI are vertical or congruent angles, then m∠HKI = 82°.

Tell me which situation matches your problem (or share the picture) and I’ll finish the solution.