Question

in circle, ( moverparen{bd}=36^{circ} ) find ( mangle bed ).( mangle bed = 144^{circ} )( mangle bed = 18^{circ} )( mangle bed = 72^{circ} )( mangle bed = 6^{circ} )

Explanation:

Step1: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.
$$m\angle BED=\frac{1}{2}m\overarc{BD}$$

Step2: Substitute the value of the arc measure

Given \(m\overarc{BD} = 36^{\circ}\), substitute into the formula.
$$m\angle BED=\frac{1}{2}\times36^{\circ}$$

Step3: Calculate the angle measure

$$m\angle BED = 18^{\circ}$$

Answer:

\(m\angle BED = 18^{\circ}\) (corresponding to the option \(m\angle BED=18^{\circ}\))