Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
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Exercise 8 Page 167

First find an expression for an angle that forms linear pairs with (6x-6).

x=9

Practice makes perfect

To find the value of x, we have to relate the two angles somehow. To do that, we will first determine an expression for the angle that forms a linear pair with (6x-6)^(∘). Linear pairs are supplementary so the other angle can be written as 180^(∘)-(6x-6)^(∘).

The new angle and (11x+33) are both above the lines and to the right of the transversal. Therefore, the angles can be classified as corresponding angles. According to the Corresponding Angles Converse, if the angles are congruent, the lines are parallel. We can write the equation 11x+33=180-(6x-6). Let's solve this equation.
11 x + 33 = 180 - 6 x + 6
11 x + 33 = 186 - 6 x
17 x + 33 = 186
17 x = 153
x = 9
When x=9, m ∥ n.