Question

In the figure below, what is the value of a?A. 9B. 12C. 12.75D. 13.5

Answer 1

By definition, an Inscribed angle of a circle is an angle whose vertex is on the circle. This can be calculated by dividing the Intercepted arc by 2.

In this case you can identify that the Inscribed angle is represented with the following expression:

`12a+6`

And the Intercepted arc is represented with this expression:

`16a+84`

Therefore, you can set up the following equation:

`12a+6=(16a+84)/(2)`

Now you can solve for "a" in order to find its value:

`\begin{gathered} (2)(12a+6)=16a+84 \\ 24a+12=16a+84 \\ 24a-16a=84-12 \\ 8a=72 \\ a=9 \end{gathered}`

The answer is: Option A.