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McGraw Hill Integrated II, 2012 View details

5. The Triangle Inequality

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Exercise 58 Page 452

Use the Alternate Exterior Angles Theorem.

x=13 by the Alternate Exterior Angles Theorem

Practice makes perfect

Let's begin by labeling the given angles.

Note that ∠ 1 and ∠ 2 are alternate exterior angles. For lines m and n to be parallel, this pair of angles must be congruent according to the Alternate Exterior Angles Theorem. m∠ 1 = m∠ 2 Finally, we substitute the measures of the angles and solve the equation for x. Note that ∠ 2 is a right angle. Therefore, m∠ 2 = 90.

m∠ 1 = m∠ 2

SubstituteII

m∠ 1= 7x-1, m∠ 2= 90

7x-1 = 90

▼

Solve for x

AddEqn

LHS+1=RHS+1

7x = 91

DivEqn

.LHS /7.=.RHS /7.

x = 13