Question

given a || b, write an equation that will help you find the value of x, if m∠4 = 3x - 7 and m∠5 = 4x - 9.
a. 3x - 7 + 4x - 9 = 90
b. 3x - 7 + 4x - 9 = 180
c. 4 + 3x - 7 = 5 + 4x - 9
d. 3x - 7 = 4x - 9

Explanation:

Step1: Identify angle - relationship

Since \(a\parallel b\), \(\angle4\) and \(\angle5\) are alternate - interior angles.

Step2: Apply alternate - interior angles theorem

Alternate - interior angles formed by two parallel lines and a transversal are congruent. So \(m\angle4=m\angle5\).

Step3: Substitute angle measures

Given \(m\angle4 = 3x - 7\) and \(m\angle5=4x - 9\), we get the equation \(3x - 7=4x - 9\).

Answer:

D. \(3x - 7 = 4x - 9\)