Answer: mBED = 2(42°) = 84°
Explanation:
We are asked to find the measure of the central angle ∠BED in the circle given that the measure of the minor arc BD is 42°.
We can use the formula that states that the measure of a central angle is equal to twice the measure of its intercepted arc. That is,
m∠BED = 2*mBD
We can substitute the value of mBD, which is 42°, into our equation.
m∠BED = 2*42°
m∠BED = 84°
Therefore, the measure of the central angle ∠BED is 84°.