Question

a) 95° mrs. healy
b) 98° mr. addison
c) 102° ms. fitzgerald
d) 105° mr. jacobs
e) 109° mrs. steele

Explanation:

Step1: Set up the equation

Vertical angles are equal. So, \(6x + 7=8x - 27\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(7 = 2x-27\).
Add \(27\) to both sides: \(34=2x\).
Divide by \(2\): \(x = 17\).

Step3: Find the measure of \(\angle ABE\)

Substitute \(x = 17\) into \(6x + 7\): \(6\times17+7=102 + 7=109^{\circ}\).

Answer:

E. \(109^{\circ}\)