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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

2. Parallel Lines and Transversals

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Exercise 2 Page 505

What kind of angle pair is ∠ 3 and ∠ 4?

x = 54

Practice makes perfect

To find the value of x, we should first find the measure of ∠ 4 which forms a linear pair with ∠ 3.

This means they are supplementary angles and add up to 180^(∘).

m ∠ 3+ m∠ 4 = 180

m ∠ 3= 68

68+ m∠ 4 = 180

LHS-68=RHS-68

m∠ 4 = 112^(∘)

Now we can use the fact that ∠ 4 and ∠ 8 are corresponding angles.

By the Corresponding Angles Theorem, they are congruent which means we can equate their measures.

m ∠ 4 = m∠ 8

m ∠ 4= 112, m ∠ 8= 2x+4

112 = 2x+4

▼

Solve for x

LHS-4=RHS-4

108 = 2x

.LHS /2.=.RHS /2.

54 = x

Rearrange equation

x = 54

Subchapter links

Communicate Your Answer p.503

Monitoring Progress p.505-506

Exercises p.507-508