The measure of ∠DCE is 50° which is the exterior angle of the circle.
It is given that the lines CD and CE are tangent to the circle.
It is required to find the measure of ∠DCE if ∠DAE = 130°
What is a circle?
It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have CD and CE are tangent to circle ∠DAE = 130°
Here we can see in the figure that ∠ECD is the exterior angle.
∠ADC = 90° and ∠AEC=90° (because AD is the perpendicular to CD)
So the measure of the ∠DCE is:
= 360 - ∠ADC - ∠AEC - ∠DAE
= 360 - 90 - 90 - 130
= 50°
Thus, the measure of ∠DCE is 50° which is the exterior angle of the circle.
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