Question

What is the value of x?

Answer 1

x=12

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

`10x + x + 61 + x + 63 + x + 80 = 360`

`13x + 204 = 360`

`13x = 156`

`x = 12`