Answer:
The measure of the arc PJ is [tex]75\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle L
we know that
In a inscribed quadrilateral opposite angles are supplementary
so
[tex]m<L+m<J=180\°[/tex]
we have
[tex]m<J=110\°[/tex]
substitute
[tex]m<L+110\°=180\°[/tex]
[tex]m<L=70\°[/tex]
step 2
Find the measure of arc KJ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<P=\frac{1}{2}(arc\ LK+arc\ KJ)[/tex]
substitute the values
[tex]95\°=\frac{1}{2}(125\°+arc\ KJ)[/tex]
[tex]190\°=(125\°+arc\ KJ)[/tex]
[tex]arc\ KJ=190\°-125\°=65\°[/tex]
step 3
Find the measure of arc PJ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<L=\frac{1}{2}(arc\ PJ+arc\ KJ)[/tex]
substitute the values
[tex]70\°=\frac{1}{2}(65\°+arc\ PJ)[/tex]
[tex]140\°=(65\°+arc\ PJ)[/tex]
[tex]arc\ PJ=140\°-65\°=75\°[/tex]
