Answer: angle AOB = 40 degrees
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Explanation:
The smaller angles AOB and BOC combine to the largest angle AOC
By the angle addition postulate, we can say,
(angleAOB) + (angleBOC) = (angleAOC)
(3x+4) + (8x-28) = 108
11x-24 = 108
11x = 108+24 .... adding 24 to both sides
11x = 132
x = 132/11 .... dividing both sides by 11
x = 12
We can use this x value to find each angle
angle AOB = 3x+4 = 3*12+4 = 40 degrees
angle BOC = 8x-28 = 8*12-28 = 68 degrees
As a check,
(angleAOB)+(angleBOC) = (40)+(68) = 108
which matches with the measure of angle AOC. This confirms our answers.
