Answer:
x=12
Step-by-step explanation:
All of the arcs have central angles.
- Arc UR central angle is 10x.
- Arc RS central angle is x+61
- Arc ST central angle is x+63
- Arc TU central angle is x+80.
Since an arc's central angle measure equal the arc measure,
- Arc UR measure 10x
- Arc RS measure x+61
- Arc ST measure x+63
- Arc TU measure x+80
A circle measures 360 degrees so all the arcs added up will equal 360
[tex]10x + x + 61 + x + 63 + x + 80 = 360[/tex]
[tex]13x + 204 = 360[/tex]
[tex]13x = 156[/tex]
[tex]x = 12[/tex]
