The measures of ∠BEC and ∠ABE are 70° and 160° respectively.
What is the theorem associated with opposite interior angles?
The sum of the opposite interior angles of a triangle is equal to the external angle.
From the figure, when we apply opposite interior angle theorem, we get:
∠EBC + ∠BCE = ∠CEF
⇒ x - 5 + 90° = 4x + 10
⇒ 3x = (85 - 10)°
⇒ x = 75/3
= 25°
∴ ∠CEF = (4*25)° + 10° = 110°
∠EBC = 25° - 5° = 20°
The sum of the angles on a straight line is 180°.
∴ ∠BEC + ∠CEF = 180°
⇒∠BEC = 180° - 110°
= 70°
Similarly, ∠ABE + ∠EBC = 180°
⇒ ∠ABE = 180° - 20°
= 160°
Therefore, we have found that the measures of ∠BEC and ∠ABE are 70° and 160° respectively.
Learn more about opposite interior angles here: https://brainly.com/question/24839702
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