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Big Ideas Math: Modeling Real Life, Grade 7

BI

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

5. Finding Unknown Angle Measures

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Exercise 33 Page 395

If three adjacent angles in the diagram form a straight angle, we know that that the sum of their measures equals 180^(∘).

∠ NJM= 25^(∘), ∠ KJL=80^(∘)

Practice makes perfect

Let's consider the given diagram.

We see that we have three adjacent angles that sum to the straight angle ∠ NJK. Therefore, the sum of their measures equals the measure of ∠ NJK — 180^(∘). Let's write this fact as an equation for x. (3x+5)^(∘)+ 75^(∘) + x^(∘) = 180^(∘) Let's solve it!

(3x+5)^(∘)+75^(∘) + x^(∘) = 180^(∘)

Add terms

4x^(∘) + 80^(∘) = 180^(∘)

LHS-80^(∘)=RHS-80^(∘)

4x^(∘) = 100^(∘)

.LHS /4.=.RHS /4.

x^(∘) = 25^(∘)

This means that ∠ NJM= 25^(∘). Now, we can substitute x=25 into (3x+5)^(∘) to find its exact value of ∠ KJL.

(3x+5)^(∘)

x= 25

(3( 25)+5)^(∘)

Multiply

(75+5)^(∘)

Add terms

80^(∘)

We found that ∠ KJL=80^(∘).

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