Exercise 13 Page 306

To find m∠ KJL, let's first consider ∠ KJM. We can see that the segments connecting L with the sides of ∠ KJM are both perpendicular to the sides. This means that their length is the distance from each side to L. Moreover, they are congruent.

According to the Converse of the Angle Bisector Theorem, if a point is in the interior of an angle and is equidistant from the two sides of the angle, then it lies on the bisector of the angle. Therefore, JL forms a bisector of ∠ KJM.

Since an angle bisector divides an angle into two congruent adjacent angles the measures of ∠ KJL and ∠ LJM are equal. This allows us to write an equation. m∠ KJL = m∠ LJM Let's substitute the given measures and solve for x.

m∠ KJL = m∠ LJM

SubstituteII

m∠ KJL= 7x, m∠ LJM= 3x+16

7x= 3x+16

▼

Solve for x

SubEqn

LHS-3x=RHS-3x

4x=16

DivEqn

.LHS /4.=.RHS /4.

x=4

We found that x=4. Let's substitute this value into the expression of ∠ KJL. 7x^(∘) → 7( 4)^(∘) → 28^(∘) Therefore, m∠ KJL=28^(∘).