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^(∘).
