Exercise 74 Page 530

Let's analyze the given rhombus. Recall that consecutive angles in a parallelogram are supplementary.

Therefore, the measures of ∠ FGH and ∠ DHG sum to 180^(∘). With this information, we can write an equation to determine ∠ DHG. m ∠ DHG+118^(∘) = 180^(∘) ⇕ m ∠ DHG=62^(∘) Note that if a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles which means it cuts them in two congruent halves.

Since ∠ MHG is half that of ∠ DHG, we can determine this angle by dividing ∠ DHG by 2. 62^(∘)/2= 31^(∘)