The bisector CF, CFD = 72 degrees, is drawn in the CDE triangle with an angle E = 32 degrees. Find D.
| September 10, 2021 | education
The EFD angle is the expanded angle, then ∠CFE = 180 – ∠CFD = 180 – 72 = 108.
Consider the triangle ECF and determine the value of the angle ECF.
∠ECF = 180 – ∠CEF – ∠CFE = 180 – 32 – 108 = 40.
Since CF is the bisector of angle C, the angle ECD = 2 * ECF = 2 * 40 = 80.
Consider a triangle CED, for which ∠CED = 320, ∠ECD = 80, then ∠CDE = 180 – 32 – 80 = 68.
Answer: Angle CDE = 80.
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