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Big Ideas Math: Modeling Real Life, Grade 7

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Big Ideas Math: Modeling Real Life, Grade 7 View details

5. Finding Unknown Angle Measures

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Exercise 7 Page 392

Vertical angles have the same measure.

m ∠ KJM = 120^(∘)

Practice makes perfect

We want to find the measure of ∠ KJM using the following diagram.

First, let's find the value of x. We notice that ∠ LJK and ∠ PJN are vertical angles, so they have the same measure.

Now, ∠ PJN and ∠ NJM are complementary angles — the sum of their measures equals 90^(∘). Let's write this fact as an equation for x and solve it!

6x^(∘)+ 12^(∘)=90^(∘)

Add terms

18x^(∘) = 90^(∘)

.LHS /18.=.RHS /18.

x^(∘) = 5^(∘)

Now that we know the value of x, let's substitute it into the expression for the measure of ∠ LJK. m ∠ LJK = 6( 5)^(∘) = 30^(∘) Let's add this value to out diagram.

Finally, let's notice that ∠ KJM is formed from two smaller angles: ∠ LJK and ∠ LJM. The first angle's measure is 30^(∘). The second angle is adjacent to a right angle ∠ PJM with which it forms a line LP — the two angles are supplementary. Therefore, its measure is 180^(∘) - 90^(∘) = 90^(∘). The measure of ∠ KJM is a sum of m ∠ LJK and m∠ LJM. m ∠ KJM = 30^(∘) + 90^(∘) = 120^(∘)

Subchapter links

Try It p.390-392

Self-Assessment for Concept & Skills p.392

Self-Assessment for Problem Solving p.393

Review & Refresh p.394

Concept, Skills, & Problem Solving p.394-396