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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Proving Angle Relationships

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Exercise 8 Page 304

What is the measure of a right angle?

Measures: m∠ 5=45, m∠ 6=45
Theorem: Supplement Theorem

Practice makes perfect

Let's begin by adding some labels to the given diagram.

Since ∠ ABC is a right angle, we know m∠ ABC=90. We can see that ∠ 5, ∠ 6, and ∠ ABC form a linear pair. Therefore, the Supplement Theorem gives us the following relation. m∠ 5 + m∠ 6 + m∠ ABC = 180 We are given that m∠ 5 = m∠ 6. With this information, we will first find the measure of m∠ 5 by substituting m∠ 6 = m∠ 5 and m∠ ABC = 90 into this equation.

m∠ 5 + m∠ 6 + m∠ ABC = 180

m∠ 6= m ∠ 5, m∠ ABC= 90

m∠ 5 + m∠ 5 + 90 = 180

Add terms

2 m∠ 5 +90=180

LHS-90=RHS-90

2 m∠ 5 = 90

.LHS /2.=.RHS /2.

m∠ 5 =45

We found that the measure of ∠ 5 is 45^(∘). Consequently, the measure of ∠ 6 is also 45^(∘).

Subchapter links

Exercises p.304-307