Answer:
130
Step-by-step explanation:
Hello There!
An included angle is equal to half the measure of its included arc
So more specifically for this circle
∠mABC = arc(mAB)
So in order to find the value of x we are going to want an equation
Because angle ABC is equal to 1/2 of arc AB we are going to want to multiply angle ABC's expression by two
So 2(3x+32) = 10x+20
now we solve for x
step 1 distribute the 2
2 * 3x = 6x
2 * 32 = 64
now we have
6x + 64 = 10x + 20
step 2 subtract 20 from each side
64 - 20 = 44
20 - 20 cancels out
now we have 6x + 44 = 10x
step 3 subtract 6 x from each side
10x - 6x = 4x
6x - 6x cancels out
now we have 44 = 4x
step 4 divide each side by 4x
44/4=11
4x/4=x
we're left with x = 11
finally we want to plug in 11 to x for (10x+20)
10(11)+20
10*11=110
110+20=130
so arc ab = 130