Question

Thank you for the help!

Answer 1

• D. 77°

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The measure of the inscribed angle is half the measure of its intercepted arc.

In our case the inscribed angle is ∠CDE. The intercepted arc is CBE, the sum of arcs BC and BE. It gives us:

• m∠CDE = (mBC + mBE)/2
• m∠CDE = (64° + 90°)/2
• m∠CDE = 77°

The matching choice is D.

Answer 2

D

Explanation:

the measure of the inscribed angle CDE is half the measure of its intercepted arc EC , that is

∠ CDE =
`(1)/(2)` × (EB + BC) =
`(1)/(2)` (90 + 64)° =
`(1)/(2)` × 154° = 77°