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.

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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 / piStep: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

Answer

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 / piStep: 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

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.

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