In circle geometry, the measure of an inscribed angle is half the measure of the corresponding intercepted arc. Given that angle \( JMK \) measures \( 82 \) degrees and that arc \( JK \) measures \( 5x - 6 \) degrees, we can set up the following equation:
\[ \frac{1}{2} \times \text{(measure of arc JK)} = \text{(measure of angle JMK)} \]
This can be expressed as:
\[ \frac{1}{2} (5x - 6) = 82 \]
To eliminate the fraction, we multiply both sides by \( 2 \):
\[ 5x - 6 = 164 \]
Next, isolate \( 5x \) by adding \( 6 \) to both sides:
\[ 5x = 164 + 6 \] \[ 5x = 170 \]
Now, divide both sides by \( 5 \):
\[ x = \frac{170}{5} \] \[ x = 34 \]
Since \( 34 \) is not among your choices (17.6, 82, 41, or 14.8), I suspect there may have been a misunderstanding or a misstatement of arc measures or angle. Please check if there are any adjustments needed in the problem statement, or if arc JK should have different parameters.
Let me know if you'd like to double-check anything or assess with different numbers!
1 answer