Step 1: Theorem
The measure of the angle between two tangent that intercept outside a circle is half the positive difference of the measure of the intercepted arcs.
Step 2: Redraw the figure.
Step 3:
We know that 2x + 240 = 360.
Collect like terms
[tex]\begin{gathered} 2x\text{ + 240 = 360} \\ 2x\text{ = 360 - 240} \\ 2x\text{ = 120} \\ \text{x = }\frac{120}{2} \\ x\text{ = 60} \end{gathered}[/tex]
The value of x can also be calculated using the formula below from the theorem.
The measure of the angle between two tangent that intercept outside a circle is half the positive difference of the measure of the intercepted arcs
[tex]\begin{gathered} \text{x = }\frac{240\text{ - 2x}}{2} \\ \text{Cross multiply} \\ 2x\text{ = 240 - 2x} \\ \text{Collect like terms} \\ 2x\text{ + 2x = 240} \\ 4x\text{ = 240} \\ \text{Divide through by 4} \\ \frac{4x}{4}\text{ = }\frac{240}{4} \\ \text{x = 60}^o \end{gathered}[/tex]
