Answer:
Part 1) [tex]m<LOQ=80\°[/tex]
Part 2) [tex]m<LRQ=40\°[/tex]
Part 3) [tex]m<LBQ=40\°[/tex]
Step-by-step explanation:
Part 1) Find the measure of angle LOQ
we know that
[tex]m<LOQ=m\ arc\ QL[/tex] -----> by central angle
we have that
[tex]m\ arc\ QL=80\°[/tex]
so
[tex]m<LOQ=80\°[/tex]
Part 2) Find the measure of angle LRQ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<LRQ=(1/2)m\ arc\ QL[/tex]
we have
[tex]m\ arc\ QL=80\°[/tex]
substitute
[tex]m<LRQ=(1/2)80\°=40\°[/tex]
Part 3) Find the measure of angle LBQ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<LBQ=(1/2)m\ arc\ QL[/tex]
we have
[tex]m\ arc\ QL=80\°[/tex]
substitute
[tex]m<LBQ=(1/2)80\°=40\°[/tex]
