Question

what is the value of x?

x = \boxed{\circ}

Explanation:

Step1: Sum of central angles is 360°

The sum of all central angles in a circle is \(360^\circ\). So we set up the equation: \((x + 56) + (x + 7) + 69 + (x + 63) = 360\).

Step2: Simplify the left - hand side

Combine like terms: \(x + 56+x + 7+69+x + 63=(x+x+x)+(56 + 7+69+63)=3x+(56 + 7+69+63)\).
Calculate \(56 + 7+69+63=(56 + 7)+(69 + 63)=63+132 = 195\). So the equation becomes \(3x+195 = 360\).

Step3: Solve for x

Subtract 195 from both sides: \(3x=360 - 195=165\).
Divide both sides by 3: \(x=\frac{165}{3}=55\).

Answer:

\(55\)