Answer: 19.0°
Step-by-step explanation:
To find the measure of the central angle given the arc length and radius, use the formula for the arc length:
\[ \text{Arc Length} = r \times \theta \]
where \( \theta \) is the central angle in radians, and \( r \) is the radius.
Given:
- Arc Length = 12 cm
- Radius (\( r \)) = 36 cm
Rearrange the formula to solve for \( \theta \):
\[ \theta = \frac{\text{Arc Length}}{r} \]
Substitute the given values:
\[ \theta = \frac{12 \text{ cm}}{36 \text{ cm}} \]
\[ \theta = \frac{1}{3} \text{ radians} \]
To convert radians to degrees, use the conversion factor \( 180^\circ / \pi \):
\[ \text{Angle} = \frac{1/3}x{180°/pi
approx 19.1°
So, the measure of the angle is approximately ( 19.1°).
