Final answer:
To find the value of x and the measure of the angle, set the two vertical angles equal to each other. Solve for x and substitute the value of x to find the measure of the angle.
Step-by-step explanation:
To find the value of x and the measure of the angle, we can set the two vertical angles equal to each other:
4x + 1 = 3x + 29
Subtracting 3x from both sides gives:
x + 1 = 29
Subtracting 1 from both sides gives:
x = 28
Therefore, x = 28. To find the measure of the angle, we can substitute x into either of the given angles:
m∠ABC = 4x + 1 = 4(28) + 1 = 113
The measure of the angle is 113 degrees.
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