how to construct a quadrilateral MATH where MT bisects M. AH is perpendicular bisector of MT. M is 60 degrees. A is 120 degrees. MH is 8cm

Answer 1

Make a sketch of your finished quad and enter all the information.
Notice that adjacent angles add up to 180°, so AT || MH, and it is easy to see that MAH must be an equilateral triangle.

You should see that MATH must be a rhombus, with all sides equal to 8 cm

I assume you know how to construct a 60° angle with compass and straightedge.
The rest is easy.