The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
We are given a ray diagram.
In the diagram, the measure of angles are given as:
∠ ACB = 25°
∠ ACG = 90°
We need to find the measure of angle ∠ DCE when CE bisects ∠ DCEF.
Now, we know that:
∠ BCG = ∠ DCF ( Vertically opposite angles.) … (1)
Now,
∠ BCG = ∠ ACB + ∠ ACG
∠ BCG = 25° + 90°
∠ BCG = 115° … (2)
∠ DCF = ∠ DCE + ∠ CEF
∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)
∠ DCF = 2 ∠ DCE … (3)
Now, put (2) and (3) in (1), we get that:
115° = 2 ∠ DCE
∠ DCE = 115 / 2°
∠ DCE = 57.5°
Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
Learn more about vertically opposite angles here:
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