Since S is the incenter of triangle PLJ, PS is the bisector of ∠P.
56^(∘)
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 is the bisector of ∠P. This means that ∠MPS and ∠SPQ are congruent.
We can write that the measure of ∠MPQ is a sum of the measures of ∠MPS and ∠SPQ.
m∠MPQ=m∠MPS +m∠SPQ
Since we are given that m∠MPS is 28^(∘), we can evaluate the measure of ∠MPQ. Remember that ∠MPS and ∠SPQ are congruent.
m∠MPQ= 28^(∘)+ 28^(∘)= 56^(∘)
The measure of ∠MPQ is 56^(∘).
