Question

(09.01 MC)
Lines CD and DE are tangent to circle A as shown below:
If arc CE is 105°, what is the measure of ∠ CDE?

Answer 1

Given info : Lines CD and DE are tangents to circle A as shown in figure. if arc CE is 105°C.

To find : the measure of ∠CDE = ?

solution : CD and DE are tangents to circle A.

so, ∠DCA = 90° and ∠DEA = 90° [ ∵ tangent is perpendicular to radius of circle. ]

and arc CE = 105°

⇒∠CAE = 105°

now from quadrilateral DCAE ,

∠CDE + ∠DCA + ∠DEA + ∠CAE = 360°

⇒∠CDE + 90° + 90° + 105° = 360°

⇒∠CDE = 180° - 105° = 75°

Therefore the measure of angle CDE is 75°.

Answer 2

∠ CDE = 75°

hope this will help u