Answer:
[tex]m\angle U=29^o[/tex]
Step-by-step explanation:
step 1
Find the measure of arc RT
we know that
The inscribed angle is half that of the arc it comprises
so
[tex]m\angle S=\frac{1}{2}[arc\ RT][/tex]
substitute the given value
[tex]21^o=\frac{1}{2}[arc\ RT][/tex]
[tex]arc\ RT=42^o[/tex]
step 2
Find the measure of angle U
we know that
The measure of the external angle is the semi-difference of the arches it covers.
so
[tex]m\angle U=\frac{1}{2}[arc\ RS-arc\ RT][/tex]
we have
[tex]arc\ RT=42^o[/tex]
[tex]arc\ RS=100^o[/tex]
substitute
[tex]m\angle U=\frac{1}{2}[100^o-42^o]=29^o[/tex]
