Question

The diagram below, MATH is a rhombus with diagonals AH and MT.
If m/HAM = 12, what is m/AMT?

Answer 1

∠ AMT = 78°

Explanation:

the diagonals of a rhombus bisect the angles , so

∠ HAT = ∠ HAM = 12° , then

∠ MAT = 12° + 12° = 24°

the sides of a rhombus are congruent , so AM = AT , thus

Δ MAT is isosceles with base angles congruent , that is

∠ AMT = ∠ ATM = (180 - 24)° ÷ 2 = 156° ÷ 2 = 78°