Answer: x = 10
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Explanation:
The angle EQD is an inscribed angle that cuts off the arc from E to D (the shortest path). Note how central angle ECD also cuts off this same arc. By the inscribed angle theorem, we know that
inscribed angle = (1/2)*(central angle)
angle EQD = (1/2)*(angle ECD)
We can multiply both sides by 2 and flip the equation to get
angle ECD = 2*(angle EQD)
Now replace "angle EQD" with 5x+2
angle ECD = 2*(5x+2)
2*(5x+2) = angle ECD
Next, replace "angle ECD" with 104 as this is the measure of this central angle.
2*(5x+2) = angle ECD
2*(5x+2) = 104
From here, we solve for x
2*(5x+2) = 104
2*5x + 2*2 = 104
10x + 4 = 104
10x+4-4 = 104-4 ..... subtracting 4 from both sides
10x = 100
10x/10 = 100/10 ...... dividing both sides by 10
x = 10
