Question

note: angles not necessarily drawn to scale. x =

Explanation:

Step1: Recall angle - sum property of a circle

The sum of angles around a point is 360°.

Step2: Set up the equation

We know that \(x + 115^{\circ}+100^{\circ}+\text{(the fourth - angle)}=360^{\circ}\). The fourth - angle is vertical to \(x\), so it is also \(x\). The equation becomes \(x + 115^{\circ}+100^{\circ}+x=360^{\circ}\).

Step3: Combine like terms

\(2x+215^{\circ}=360^{\circ}\).

Step4: Solve for \(x\)

First, subtract \(215^{\circ}\) from both sides: \(2x=360^{\circ}- 215^{\circ}=145^{\circ}\). Then divide both sides by 2: \(x = 72.5^{\circ}\).

Answer:

\(72.5\)