Based on the definition of supplementary angles, the value of x is: 47.
What are Supplementary Angles?
Angles AOB and BOD are angles on a straight line, therefore, they are supplementary angles. Hence, we have:
Given the following:
measure of angle AOB. = 2x − 4)°
Measure of angle BOD = (14x + 12)°
measure of angle AOB + measure of angle BOD = 180
Substitute the values into the equation
2x - 4 + 2x - 4 = 180
Combine like terms
4x - 8 = 180
Add 8 to both sides of the equation
4x = 180 + 8
4x = 188
Divide both sides of the equation by 4
4x/4 = 188/4
x = 47
Thus, based on the definition of supplementary angles, the value of x is: 47.
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