Given: circle k(O), m∠P=95°, m∠J=110°, m∠LK=125° Find: m∠PJ

Answer:The measure of the arc PJ is [tex]75\°[/tex]Step-by-step explanation:step 1Find the measure of angle Lwe know thatIn a inscribed quadrilateral opposite angles are supplementaryso[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 2Find the measure of arc KJwe know thatThe inscribed angle measures half that of the arc comprisingso[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 3Find the measure of arc PJwe know thatThe inscribed angle measures half that of the arc comprisingso[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]