Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
1. Angles of Triangles
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Exercise 50 Page 594

What pair of angles are 118^(∘) and x^(∘)?

x^(∘)=118^(∘) y^(∘)=96^(∘)

Practice makes perfect

If we highlight relevant parts of the figure, we can make out a transversal that cuts two parallel lines.

According to the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, then the pair of corresponding angles are congruent. x^(^(∘))=118^(∘). When we know the measure of x^(∘), we can use the Exterior Angle Theorem to find y^(∘). The theorem says that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. y^(∘)+22^(∘)=118^(∘) By solving this equation we can find the measure of y^(∘).
y^(∘)+22^(∘)=118^(∘)
y^(∘)=96^(∘)
The measure of y^(∘) is 96^(∘).