Final answer:
To find the measure of angle AOB, we add the measures of AOC and BOC and subtract from 360° to find x, then use x to calculate m∆AOB, which is approximately 72.73°.
Step-by-step explanation:
To find m∆AOB, which stands for the measure of angle AOB, we can use the fact that the sum of angles around a point is 360°. Given that m∆AOC = 108°, m∆AOB = 3x + 4°, and m∆BOC = 8x - 28°, we can create an equation based on the sum of these angles:
m∆AOB + m∆BOC + m∆AOC = 360°
(3x + 4°) + (8x - 28°) + 108° = 360°
Combining like terms, we get:
11x - 24° = 360° - 108°
11x = 252°
x = 252° / 11
x ≈ 22.91°
Now we plug x back into the expression for m∆AOB:
m∆AOB = 3(22.91°) + 4° ≈ 68.73° + 4° ≈ 72.73°
Therefore, m∆AOB ≈ 72.73°.