Answer:
[tex]arc\ RS=136\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
In this problem
m∠RPS=[tex]26\°[/tex] ------> external angle
so
m∠RPS=[tex]\frac{1}{2}(arc\ RS-arc\ SQ)[/tex]
we have
m∠RPS=[tex]26\°[/tex]
[tex]arc\ SQ=84\°[/tex]
substitute the values
[tex]26\°=\frac{1}{2}(arc\ RS-84\°)[/tex]
Solve for arc RS
[tex]52\°=(arc\ RS-84\°)[/tex]
[tex]arc\ RS=52\°+84\°=136\°[/tex]
