Question

Lines CD and DE are tangent to circle A as shown below: If CE is 105 degrees, what is the measure of angle CDE?

Answer 1

Answer:

C

Step-by-step explanation:

∠CDE = 0.5( mEC - m CE )

The arcs CE and EC must add to 360°, thus

arc EC = 360° - 105° = 255°, hence

∠CDE = 0.5(255 - 105)° = 0.5 × 150° = 75° → C

Answer 2

Answer:75°

Step-by-step explanation:

Using the outside angle theorem

<CDE = CBE - EC / 2

arcCE = 105°

but we dont know that of CBE

we can find it by subtracting EC from 360° (angle of a circle is 360°, so we simply subtract the part EC from it to get CBE)

CBE =360 - 105 = 255°

<CDE = CBE - EC / 2

= 255° - 105° / 2

= 150° / 2

=75°

Therefore angle CDE is 75 degrees.