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Lines CD and DE are tangent to circle A shown below. If CE is 112°, what is the measure of ∡CDE?

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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

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Other answers:

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

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