Question

what is the value of x?
there is a circle with center w. there are several angles at the center: ( x + 58^circ ), ( 86^circ ), ( 90^circ ), ( x - 14^circ ), and the lines connect to points t, u, v, s respectively. at the bottom, there is a box to fill in the value of x with ( x = square^circ )

Explanation:

Step1: Sum of central angles is 360°

The sum of all central angles in a circle is \( 360^\circ \). So, we have the equation: \((x + 58)^\circ+(x - 14)^\circ+90^\circ+86^\circ = 360^\circ\)

Step2: Simplify the equation

Combine like terms: \(2x + 58 - 14 + 90 + 86 = 360\)
\(2x + 220 = 360\)

Step3: Solve for x

Subtract 220 from both sides: \(2x = 360 - 220 = 140\)
Divide by 2: \(x=\frac{140}{2}=70\)

Answer:

\(70\)