The measure of angle DCF will be 129°.
An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given,
∠DCE = 75°
∠ECF = 54°
Now,
∠DCF = ∠DCE + ∠ECF
∠DCF = 75 + 54
∠DCF = 129°
Hence, the measure of angle DCF will be 129°.
For more about the angle,
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