Angles in a circle

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In the following diagram, the radius is 24 cm and $\angle$ $∠$ BDC is 75°.
1. Find $\angle$ BAC.
2. Find the chord BC.
You are setting up a display board for the science fair. You have two spotlights: one projects through an angle of 20°; and one projects through an angle of 40°. Where is the best place to put the display board? Show your answer in a diagram.
Given $\angle$ $∠$ BAE = 44.5° and $\angle$ $∠$ ADC = 64.27°.

Find.
1. $\angle$ BCD
2. $\angle$ AEB
3. $\angle$ CED