Answer:
∠CDE = 82° (last option)
Explanation:
Given:
arc CE is 98°
Lines CD and DE are tangent to circle A
To find:
the measure of ∠CDE
To determine angle CDE, we will apply the theorem relating the tangent to outside angle:
[tex]\begin{gathered} ∠CDE\text{ = }\frac{1}{2}(larger\text{ arc - smaller arc\rparen} \\ larger\text{ arc = arc CBE} \\ smaller\text{ arc = arc CE = 98\degree} \end{gathered}[/tex]
We need to find the measure of the larger arc:
Arc CE + arc CBE = 360° (sum of angles in a triangle)
arc CBE = 360 - 98
arc CBE = 262°
substitute the measures into the formula:
[tex]\begin{gathered} ∠CDE\text{ = }\frac{1}{2}(262\text{ - 98\rparen} \\ \\ ∠CDE=\text{ }\frac{1}{2}(164) \\ \\ ∠CDE\text{ = 82\degree} \end{gathered}[/tex]
