Angle f is 146 degrees
Explanation:
Hello! Recall that you have to post complete questions in order to get good and correct answer. However, I have attached a figure below that I think represents the statement of your problem.
In this case, we can set the following equations:
(1) ∠d = (3x + 7)°
(2) ∠e = (4x - 2)°
These two angles are Alternate interior angles. They are interior angles because they're between the parallel lines ([tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex]) and they are alternate angles because they're on different sides of the transversal line (The third one that passes through the parallel lines)
Alternate interior angles are always congruent to each other, so this means they have the same measure. In other words:
∠d = ∠e
(3x + 7)° = (4x - 2)°
Isolating x:
3x + 7 = 4x - 2
Combine like terms:
7 + 2 = 4x - 3x
9 = x
x = 9
So:
∠e = (4x - 2)°
∠e = [4(9) - 2]°
∠e = [36 - 2]°
∠e = 34°
∠e and ∠f are supplementary angles meaning they add up to 180 degrees, so:
∠e + ∠f = 180°
Isolating ∠f:
34°+ ∠f = 180°
∠f = 180° - 34°
∠f = 146°
Learn more:
Complementary angles: https://brainly.com/question/12254549
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