Question

Lines CD and DE are tangent to circle A, as shown below:

Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 110 degrees. Point B lies on circle A.

If arc CE is 110°, what is the measure of ∠CDE?

55°
70°
100°

Answer 1

Using the outside angle theorem, the measure of angle CDE is: 70°.

How to Apply the Angle of Intersecting Tangents Theorem?

According to the angle of intersecting tangents theorem, we would have the following equation using the diagram given:

Angle CDE = ½(measure of arc CBE - measure of arc CE)

Given the following:

• Measure of arc CE = 110°
• Measure of arc CBE = 360 - 110 = 250°

Plug in the values into the equation

Angle CDE = ½(250 - 110)

Angle CDE = 70°

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