Question

Find the measure of

Answer 1

∠ ADE = 55° , ∠ ACE = 32.5° , ∠ BAD = 22.5°

Explanation:

the measure of the inscribed angle ADE is half the measure of its intercepted arc AE , then

∠ ADE =
`(1)/(2)` × 110° = 55°

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the measure of the secant- secant angle ACE is half the difference of the measures of the intercepted arcs , that is

∠ ACE =
`(1)/(2)` (AE - BD) =
`(1)/(2)` (110 - 45)° =
`(1)/(2)` × 65° = 32.5°

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the measure of the inscribed angle BAD is half the measure of its intercepted arc BD , that is

∠ BAD =
`(1)/(2)` × 45° = 22.5°