The supplement of < 72 has the same measure as < (4x + 8). Therefore, < (4x + 8) must equal 108°. We can establish the following equality statement to solve for x:
< (4x + 8) + < 72° = 180°
Combine like terms: 4x + 80 = 180°
Subtract 80 from both sides:
4x + 80° - 80° = 180° - 80°
4x = 100
Divide both sides by 4 to solve for x:
4x/4 = 100/4
x = 25
To verify whether the value of x is correct, substitute its value into the equality statement:
< (4x + 8)° + < 72° = 180°
< [4(25) + 8]° + < 72° = 180°
< (100 + 8)° + < 72° = 180°
< 108° + < 72° = 180°
180° = 180° (True statement. Therefore, the correct answer is x = 25).
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