Answer:
x = 8
Step-by-step explanation:
< (7x - 4)° and < (3x + 28)° are Alternate interior angles that do not have a common vertex on alternate sides of the transversal, t. Therefore, they have the same measure.
We can establish the following equality statement to solve for x :
< (7x - 4)° = < (3x + 28)°
Subtract 3x from both sides:
7x -3x - 4 = 3x - 3x + 28
4x - 4 = 28
Add 4 to both sides:
4x - 4 + 4 = 28 + 4
4x = 32
Divide both sides by 4 to solve for x:
4x/4 = 32/4
x = 8.
To verify whether the value of x is correct, substitute x = 8 into the equality statement:
< (7x - 4)° = < (3x + 28)°
< [(7(8) - 4]° = < [3(8) + 28]°
< (56 - 4)° = < (24 + 28)°
< 52° = < 52° (True statement. Therefore, the correct answer is x = 8).
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