Exercise 13 Page 345

We want to find the value of x in the given diagram. Let's start by labeling the vertices of the given quadrilateral.

Because of the angle markings, we can see that ∠KJL and ∠MJL are congruent. This means that JL is the angle bisector of ∠KJM. Let's recall the Angle Bisector Theorem.

Angle Bisector Theorem

If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.

Since L is on the bisector of ∠KJM, it is equidistant from JK and JM. Also, the distance from a point to a line is the length of the perpendicular segment from the point to the line. Therefore, KL=ML. KL=ML ⇒ 5x-8= 2x+13 Let's solve the above equation to find the value of x.

5x-8=2x+13

AddEqn

LHS+8=RHS+8

5x=2x+21

SubEqn

LHS-2x=RHS-2x

3x=21

DivEqn

.LHS /3.=.RHS /3.

x=7