If the measure of a tangent-chord angle is 74, then what is the measure of the intercepted arc inside the angle?A.286B.74C.37D.148SUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify the relationship between the tangent-chord angle and the intercepted arc.
2. Apply the appropriate formulas.

Relevant Concepts

• The measure of a tangent-chord angle is half the measure of the intercepted arc.
• If $m$ is the measure of the tangent-chord angle and $m$ is the measure of the intercepted arc, the formula is: $m = \frac{1}{2} \cdot \text{(measure of the intercepted arc)}$

Analysis and Detail

1. Given that the measure of the tangent-chord angle is $74^\circ$: $74 = \frac{1}{2} \cdot x$ where $x$ is the measure of the intercepted arc.

2. To find $x$, we can rearrange the equation: $x = 74 \times 2$ $x = 148$

Verify and Summarize

• The measure of the intercepted arc, when calculated, equals $148^\circ$.
• We can double-check our calculation:
  • Since half of $148^\circ$ should give us the angle measure, $\frac{148}{2} = 74^\circ$, which confirms our calculation is correct.

Final Answer

The measure of the intercepted arc inside the angle is $148^\circ$. The correct option is D.