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Answer:

∠ CFE and ∠ DFE are adjacent angles and are supplementary, sum to 180°

∠ CFE + 152° = 180° ( subtract 152° from both sides )

∠ CFE = 28°

Step-by-step explanation:

Adjacent angles share the common side as well as a common vertex (corner point), and they do not overlap. If we decompose the term "adjacent angles".

Adjacent angles:

  • Its common side and vertex will be shared by the adjacent angles.
  • If the total of two angles equals 180°, they are said to be supplementary angles.
  • A linear pair is created when two additional angles are next to one another. 180° is equal to the sum of two adjacent supplementary angles.

We have,

∠ EFD = 152°

∠ CFE and ∠ DFE are adjacent angles and are supplementary, summing to 180°

⇒ ∠CFE + ∠EFD = 180° (Linear pair)

⇒ ∠CFE +152° = 180°

⇒ ∠CFE= 180°-152°

⇒ ∠CFE= 28°

Find out more about the adjacent angles here:

brainly.com/question/12838185