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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 68 Page 637

Use the Triangle Angle-Sum Theorem.

50

Practice makes perfect

We want to find the measure of ∠ 3 in the given figure. We have been given measures of the two angles of the figure, m ∠ DGF and m ∠ AGC. The measures of ∠ 1 and ∠ 2 were discovered in the previous exercises.

We will find m ∠ 3 using the following theorem.

Interior Angles Theorem
The measures of the interior angles of a triangle must add to 180^(∘).

Using that, we can write an equation. m∠ BGC + m ∠ 3 + m ∠ CBG = 180^(∘) Let's substitute the known values to solve it for m∠ 3 .

m∠ BGC + m ∠ 3 + m ∠ CBG = 180

m∠ BGC= 40, m ∠ CBG= 90

40 + m ∠ 3 + 90 = 180

Add terms

m ∠ 3 + 130 = 180

LHS-130=RHS-130

m ∠ 3 = 50

The measure of m ∠ 3 is 50^(∘).

Subchapter links

Exercises p.633-637