Question

What is m∠HLK? thanks

Answer 1

The answer is 80°.

If there is a line segment in a triangle which cuts two sides in half or if there is a line segment between two midpoints of a triangle's sides, that line segment must be parallel to the remaining side.

In this case, point L is the midpoint of FH, and point K is the midpoint of HG. So, LK is parallel to FG.

When a line cuts two parallel lines, there are angle pairs which are equal. In the problem above, the line segment FH cuts KL and GF.

The angles KLH and GFH are what we called "Corresponding Angles" and they are equal.

So if HFG is 80°, HLK must be equal to 80°