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Art [367]
3 years ago
14

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°

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:

55°

Step-by-step explanation:

Given that;

Lines CD and DE are tangent to circle A and intersect at point D.

and:

Arc CE measures 125 degrees. Point B lies on circle A.

There lies a diagrammatic representation below given a clear picture of what this question looks like;

If arc CE is 125°, what is the measure of ∠CDE?

SO, by using the outside angle theorem

∠CDE = \frac{CBE-CE}{2}

where arc CE = 125°

we can determine CBE  by subtracting it from angle of a circle = 360°

Thus, CBE = 360° - 125°

CBE = 235°

Again; ∠CDE = \frac{CBE-CE}{2}

∠CDE = \frac{235^0-125^0}{2}

∠CDE = \frac{110^0}{2}

∠CDE = 55°

∴ The measure of ∠CDE = 55°

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