Question

Angle ABC is bisected by line segment AD. If angle ABC measures 108° and one of the smaller angles created by line AD measures (5x+4), what is the value of x?

Answer 1

x = 10

Explanation:

One of the smaller angles that is created by the angle bisector measures 5x+4.

An angle bisector cuts an angle into two equal parts. So, 5x+4 = 1/2 (108) or

2(5x+4)=108 (divide both sides by 1/2)

10x+8=108 (distribute)

10x=100 (subtract 8 from both sides)

x=10 (divide by 10)

x=10