Question

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



If CE is 112°, what is the measure of ∡CDE?

Answer 1

picture?

Answer 2

Angle on outside of a circle is 1/2 difference of the arcs. One of the arcs is 112 (given). Other is 360 - 112 = 248 because there are 360 degrees in a circle. Setting up our equation,

ans = (1/2)(248 - 112) = (1/2)(136)
m∡CDE = 68 degrees

Answer 3

a little construction to find the angle

join AC and AE

to form a kite.. AC = AE equal radii and

DC = CE tangents from an external point are equal

Angle ACD = angle AED both 90... tangent and radius intersect at right angles

Angle CAE = 112 angle subtended by the arc CE

then ANgle CDE = 360 - 90-90 -112 angle sum of a quadrilateral

angleCDE = 68