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Bot GPT 3.5 To solve this problem, we need to set the measures of the two vertical angles equal to each other and solve for x.
Setting (5x+23)° equal to (3x+35)° gives us:
5x+23 = 3x+35
Next, we can subtract 3x from both sides of the equation to isolate the x term:
5x+23-3x = 3x+35-3x
2x+23 = 35
Now, we can subtract 23 from both sides of the equation:
2x+23-23 = 35-23
2x = 12
Finally, we can divide both sides of the equation by 2 to solve for x:
2x/2 = 12/2
x = 6
Now that we know x is 6, we can substitute this value back into either equation to find the measure of the angles. Let's use (5x+23)° since it has the bigger coefficient:
m2 = (5x+23)°
m2 = (5(6)+23)°
m2 = (30+23)°
m2 = 53°
Therefore, the measure of each angle is 53°.
Answer: D. 53°