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 125 degrees. Point B lies on circle A. If arc CE is 125°, what is the measure of ∠CDE? 55° 62.5° 117.5° 125°

Answer 1

The measure of angle CDE ( ∠CDE) is 55°. The correct option is the first option  55°

Calculating the measure of the angle formed by two tangents

From the question, we are to determine the measure of angle CDE.

From one of the circle theorems, we have that

"The measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs"

Thus,

m ∠CDE = 1/2(measure of arc CBE - measure of arc CE)

From the given information,

Measure of arc CE = 125°

Then,

Measure of arc CBE = 360° - 125°

Measure of arc CBE = 235°

Therefore,

m ∠CDE = 1/2(235° - 125°)

m ∠CDE = 1/2(110°)

m ∠CDE = 55°

Hence, the measure of ∠CDE is 55°

Learn more on Calculating the measure of the angle formed by two tangents here: brainly.com/question/9143293

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