Answer:
The measure of angle KSP is [tex]137\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle ISP
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]m<ISP=\frac{1}{2}(arc\ VK+arc\ IP)[/tex]
we have
[tex](arc\ VK+arc\ IP)=86\°[/tex]
substitute
[tex]m<ISP=\frac{1}{2}(86\°)=43\°[/tex]
step 2
Find the measure of angle KSP
we know that
[tex]m<ISP+m<KSP=180\°[/tex] ----> by supplementary angles
we have
[tex]m<ISP=43\°[/tex]
substitute
[tex]43\°+m<KSP=180\°[/tex]
[tex]m<KSP=180\°-43\°=137\°[/tex]
