Circle $O$ shown below has a radius of 10 inches. Find, to the nearest tenth of a degree, the measure of the angle, $x$, that forms an arc whose length is 26 inches.
Answer
The measure of angle x, to the nearest tenth of a degree, is \( \boxed{149.0} \) degrees
Step 1 ：Given a circle with radius 10 inches and an arc length of 26 inches, we can use the formula for arc length: Arc length = radius * angle (in radians)
Step 2 ：Convert the angle from radians to degrees using the conversion factor: 1 radian = 180 degrees / pi
Step 3 ：Set up the equation: 26 = 10 * x (in radians)
Step 4 ：Convert x to degrees and solve for x: \( x = \frac{26}{10} \cdot \frac{180}{\pi} \)
Step 5 ：Calculate x: \( x \approx 149.0 \)
Step 6 ：The measure of angle x, to the nearest tenth of a degree, is \( \boxed{149.0} \) degrees
