Question

An angle is inscribed in the circle, as shown. The degree measuresof three arcs are shown in the diagram. What is the value of x?

Answer 1

Let us begin by redrawing the circle showing the angles properly:

Using the circle theorem below, we can find the value of x:

Angle subtended at center = 2 times angle subtended at circumference

The angle at center we are interested in is 110 degrees

Angle x is the angle at circumference. Hence, we can use the theorem above:

$\begin{gathered} 110\text{ = 2 }\times x\text{ } \\ x\text{ = }\frac{110}{2} \\ x=55^0 \end{gathered}$

Answer: 55 degrees (Option A)