Since < (7x + 9) is an interior angle and < (9x - 23) an exterior angle — these angles are on the same side of the transversal, line t. Therefore, they are corresponding angles with the same measure.
Hence, we can establish the following equality statement to solve for x:
< (7x + 9) = < (9x - 23)
Subtract 7x from both sides:
7x - 7x + 9 = 9x - 7x - 23
9 = 2x - 23
Add 23 on both sides:
9 + 23 = 2x - 23 + 23
32 = 2x
Divide both sides by 2 to solve for x:
32/2 = 2x/2
16 = x
Therefore, x = 16.
Substitute x = 16 into the equality statement to verify whether it is the correct value:
< (7x + 9) = < (9x - 23)
7(16) + 9 = 9(16) - 23
112 + 9 = 144 - 23
121 = 121 (True statement. Therefore, x = 16 is the correct answer).
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