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Vertical angles are always congruent, which means they have the same measure. Therefore, we can set the two expressions for the angles equal to each other and solve for x:
5x + 23 = 3x + 35
2x = 12
x = 6
Now that we know x, we can substitute it back into either expression to find the measure of each angle:
<2 = 5x + 23 = 5(6) + 23 = 53 degrees
<4 = 3x + 35 = 3(6) + 35 = 53 degrees
Therefore, each angle measures 53 degrees.