Sector Angle 26C1A8

1. **State the problem:** We have a sector $ABCO$ of a circle with radius $R$. The length of the arc $AB$ is given as $\frac{1}{2}R$. We need to find the angle $AOB$ in degrees. 2. **Formula for arc length:** The length of an arc $s$ of a circle is related to the radius $R$ and the central angle $\theta$ (in radians) by the formula: $$ s = R \theta $$ where $\theta$ is in radians. 3. **Given:** $$ s = \frac{1}{2} R $$ Substitute into the formula: $$ \frac{1}{2} R = R \theta $$ 4. **Solve for $\theta$:** Divide both sides by $R$: $$ \frac{\cancel{R}}{2} = \cancel{R} \theta \implies \theta = \frac{1}{2} $$ So the central angle $\theta$ in radians is $\frac{1}{2}$. 5. **Convert radians to degrees:** Recall that: $$ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} $$ Therefore: $$ \theta = \frac{1}{2} \times \frac{180}{\pi} = \frac{90}{\pi} $$ 6. **Final answer:** The angle $AOB$ in degrees is: $$ \boxed{\frac{90}{\pi} \text{ degrees}} $$ This is approximately $28.65$ degrees.