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McGraw Hill Integrated II, 2012 View details

5. Rhombi and Squares

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Exercise 1 Page 517

Opposite angles in a parallelogram are congruent.

32

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Let's analyze the given rhombus.

Notice that ∠ BCD is opposite to ∠ BAD. Since a rhombus is a parallelogram, its opposite angles are congruent. This means that their measures are equal. m ∠ BCD = m ∠ BAD We already know that m ∠ BCD = 64^(∘). Substituting this into the above equation, we get that m ∠ BAD= 64^(∘) as well. Recall that in a rhombus, the diagonals bisect the angles. Therefore AC bisects ABCD. So the measure of ∠ BAC is half of the measure of ∠ BAD. ∠ BAC=(1/2)64=32