Question

If the measure of arc BC is 182 degrees and the measure of arc AC is 78 degrees, what is the measure of angle 1?Answer choice:A)52 degreesB)91 degreesc)104 degreesD)78 degrees

Answer 1

Given:

There are given that the arc of BC is 182 degrees and the measure of arc AC is 78 degrees.

Explanation:

To find the value of the angle of 1, we need to use the circle properties:

So,

From the properties:

$1=\frac{(BC-AC)}{2}$

Then,

Put the values into the above formula:

So,

$\begin{gathered} 1=\frac{(BC-AC)}{2} \\ 1=\frac{(182-78)}{2} \\ 1=\frac{104}{2} \\ 1=52 \end{gathered}$

Final answer:

Hence, the correct option is A.