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

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°