Question

Given: m∠3 = (3x − 20)° and m∠7 = (2x + 30)°

What value of x will prove that the horizontal lines are parallel?

Answer 1

x = 50

Explanation:

• The left side of the triangle is a traversal as it separates the two parallel lines.

• When two lines are parallel and cut by a traversal, corresponding angles are made.

• These types of angles are formed in the matching corners or corresponding corners with the transversal.
• They are always congruent.

• Thus, in order for the two lines to be parallel, m∠3 must equal m∠7.

Thus, we can find the value of x proving the horizontal lines are parallel by setting the two expressions representing the measures of angles 3 and 7 equal to each other:

(3x - 20 = 2x + 30) + 20

(3x = 2x + 50) - 2x

x = 50

Thus, 50 is the value of x proving that the horizontal lines are parallel.