What does the Perpendicular Transversal Theorem say?
x = 8
Practice makes perfect
Note that we have been given some extra information in the exercise. We can solve for the value of x using only the fact that the expression a ⊥ b means that a and b are perpendicular lines. Let's show this in our figure.
Now, because these lines are perpendicular, we know that marked is equal to 90^(∘) and so is the expression included in the diagram.
9x+18=90
Let's solve for x.
Solve for x using the Perpendicular Transversal Theorem
Rather than setting 9x+18 equal to 90^(∘), we can solve for the value of x by also thinking about what we know from the relationship between lines b and c.
We know that b ∥ c meaning that b and c are parallel lines. According to the Perpendicular Transversal Theorem, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.
Finally, since b and c are parallel lines, we can by the Alternate Exterior Angles Theorem, say that (9x+18)^(∘) and [5(x+7)+15]^(∘) are congruent. Therefore, we can equate them.
9x+18=5(x+7)+15
Let's solve the equation.
