Answer:
∠ CDE = 54°
Step-by-step explanation:
The measure of the tangent- tangent angle CDE is half the difference of the intercepted arcs.
∠ CDE = [tex]\frac{1}{2}[/tex] (EBC - CE )
arc EBC = 360° - 126° = 234° , then
∠ CDE = [tex]\frac{1}{2}[/tex] (234 - 126)° = [tex]\frac{1}{2}[/tex] × 108° = 54°
Lines CD and DE are tangent to circle A. If CE IS 126 .Therefore the measure of angle CDE is 75°.
Let, the lines CD and DE exists tangents to circle A as shown in figure. if arc CE exists 105°C.
Let, CD and DE are tangents to circle A.
So, ∠DCA = 90° and ∠DEA = 90° [ ∵ tangent exists perpendicular to radius of circle. ]
and arc CE = 105°
⇒ ∠CAE = 105°
From quadrilateral DCAE ,
∠CDE + ∠DCA + ∠DEA + ∠CAE = 360°
⇒ ∠CDE + 90° + 90° + 105° = 360°
⇒ ∠CDE = 180° - 105° = 75°
Therefore the measure of angle CDE is 75°.
To learn more about measure of angle
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