Answered

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

Lines CD And DE Are Tangent To Circle AIf Arc CE Is 98 What Is The Measure Of CDE 56 49 131 82 class=

Sagot :

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]

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