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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Parallelograms

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Exercise 34 Page 491

Recall that vertical angles are congruent.

72

Practice makes perfect

Let's find the measure of ∠ DAC. It will take us a few steps.

Notice that ∠ AFD and ∠ BFC are vertical angles. According to the vertical angles theorem, they are congruent.

m∠ AFD = m ∠ BFC ⇕ m∠ AFD = 49 Since ∠ DAF and ∠ DAC measure the same, it will suffice to find m∠ DAF. To do that, we will use the following theorem.

Interior Angles Theorem
The sum of the interior angles of a triangle is 180^(∘).

Therefore, we can write an expression for the angles of △ DAF. m∠ AFD + m ∠ FDA + m ∠ DAF = 180 ⇕ 49 + 59 + m ∠ DAF = 180 Now, let's solve it!

49 + 59 + m ∠ DAF = 180

Add terms

108 + m ∠ DAF = 180

LHS-108=RHS-108

m ∠ DAF = 72

Since ∠ DAF ≅ ∠ DAC, we have found that m∠ DAC = 72.

Subchapter links

Exercises p.489-493