Question

Lines CD and DE are tangent to circle AIf arc CE is 98°, what is the measure of ∠CDE? 56° 49° 131° 82°

Answer 1

Answer:

∠CDE = 82° (last option)

Step-by-step 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:

`\begin{gathered} ∠CDE\text{ = }(1)/(2)(larger\text{ arc - smaller arc\rparen} \\ larger\text{ arc = arc CBE} \\ smaller\text{ arc = arc CE = 98\degree} \end{gathered}`

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:

`\begin{gathered} ∠CDE\text{ = }(1)/(2)(262\text{ - 98\rparen} \\ \\ ∠CDE=\text{ }(1)/(2)(164) \\ \\ ∠CDE\text{ = 82\degree} \end{gathered}`