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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 74 Page 530

Consecutive angles in a parallelogram are supplementary.

31^(∘)

Practice makes perfect

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^(∘)

Subchapter links

Exercises p.526-530