To determine the measure of the intercepted arc inside a tangent-chord angle, we need to apply a specific property related to tangent-chord angles in a circle.
A tangent-chord angle is formed by a tangent and a chord that intersect at the point of tangency on a circle. The crucial property we use here is:
The measure of an intercepted arc is twice the measure of the tangent-chord angle.
Given that the measure of the tangent-chord angle is [tex]\( 54^{\circ} \)[/tex], we can find the measure of the intercepted arc by following these steps:
1. Write down the measure of the tangent-chord angle, which is [tex]\( 54^{\circ} \)[/tex].
2. Using the property mentioned, multiply the measure of the tangent-chord angle by 2 to find the intercepted arc measure.
[tex]\[
\text{Intercepted arc measure} = 2 \times \text{tangent-chord angle}
\][/tex]
3. Substitute the given angle measure into the formula:
[tex]\[
\text{Intercepted arc measure} = 2 \times 54^{\circ}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Intercepted arc measure} = 108^{\circ}
\][/tex]
Therefore, the measure of the intercepted arc is [tex]\( 108^{\circ} \)[/tex].
So, the correct answer is:
A. [tex]\( 108^{\circ} \)[/tex]
