Find mBD using the fact that AE and AC are secant to the circle and intersect each other outside it. Then, use the Arc Addition Postulate to rewrite mBC.
mDE=98^(∘)
Practice makes perfect
Let's begin by making a diagram where we label the given measures.
Since BC is a diameter of the circle we have that mBC=180^(∘). Additionally, the Arc Addition Postulate allows us to write the following equation.
mBC = m BD + m DE + m EC
To find m BD, we use the fact that AE and AC are secant to the circle and they intersect each other outside it. Thus, we can write the following equation.
m∠ A = 1/2(m EC - m BD)
Next, we substitute the corresponding measures into the equation above and solve it for m BD.
