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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. The Pythagorean Theorem and Its Converse

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Exercise 67 Page 637

Use the Triangle Angle-Sum Theorem.

50

Practice makes perfect

We want to find the measure of ∠ 2 in the given figure. We have been given measures of the two angles of the figure, m ∠ DGF and m ∠ AGC, and the measure of ∠ 1 was discovered in the previous exercise.

Note that m ∠ 2 and m ∠ AGC are complementary. m ∠ 2 + m∠ AGC = 90^(∘) Let's substitute the known value to solve the equation for m∠ 2 .

m ∠ 2 + m∠ AGC = 90

m∠ AGC= 40

m ∠ 2 + 40 = 90

LHS-40=RHS-40

m ∠ 2 = 50

The measure of m ∠ 2 is 50^(∘).

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Exercises p.633-637