Question

What is value of x? Enter your answer in the box. x =

Answer 1

Answer:

x = 27

Step-by-step explanation:

There is a point in the figure that has no name. It is the point on segment BC,  between B and C. Call that point D.

Angles BAD and CAD are shown to be congruent. That makes AD the bisector of angle ABC. Now you can use the Triangle Angle Bisector Theorem. This theorem gives you a proportion of side lengths.

AB/BD = AC/CD

Substitute the side lengths and solve for x.

(x + 8)/10 = (2x - 5)/14

14(x + 8) = 10(2x - 5)

14x + 112 = 20x - 50

-6x = -162

x = 27