Question

HELP!!!!!

Lines CD and DE are tangent to circle A shown below:

Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 98 degrees. Point B lies on circle A.

If Arc CE is 98°, what is the measure of ∠CDE?

56°
49°
131°
82°

Answer 1

82°

Explanation:

whenever a line is tangent to a circle, the line segment you can draw from the center to the tangent line on the circumference is always perpendicular, so angle ACD is 90° and angle AED is 90° and we already know CAE is 98° so adding the tree would result in 278° because ACDE forms a quadrilateral it's angle have a sum of 360° so subtract 278 from 360 and you get 82°

Answer 2

Answer: 82°

Explanation:

<CDE = far arc - near arc / 2

i.e

<CDE = arcCBE - arcCE / 2

arcCE = 98°

arcCBE = 360° - 98° = 262°

<CDE = 262° - 98° / 2

<CDE = 164 / 2

<CDE = 82°

Therefore the measure of < CDE is 82°