Since S is the incenter of triangle PLJ, SJ is the bisector of ∠ J.
37.5^(∘)
Practice makes perfect
Let's begin with recalling the Incenter Theorem.
The angle bisectors of a triangle
intersect at a point called the incenter
that is equidistant from the sides of the triangle.
Since we are given that S is the incenter of triangle PLJ, PS, LS and JS are the bisectors of ∠ P, ∠ L and ∠ J respectively.
Since we are given that m∠ MPS is 28^(∘) and m∠ SLK is 24.5^(∘), we can evaluate m∠ P and m∠ L by multiplying the given angle measures by 2.
m∠ P=2* 28^(∘)=56^(∘)
m∠ L=2* 24.5^(∘)=49^(∘)
Now, using the fact that the sum of the measures of each triangle is 180^(∘), we will evaluate m∠ J.
The measure of ∠ J is 75^(∘). Since SJ divides this angle into two congruent angles, the measure of ∠ SJP will be one half of the measure of 75^(∘).
m∠ SJP=1/2*75^(∘)=37.5^(∘)
The measure of ∠ SJP is 37.5^(∘).
