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Answer :

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 = [tex]\frac{1}{2}[/tex] 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

SWEETEANY34GO

Answer:

AB = 130

Step-by-step explanation:

So, according to a certain theorem to do with arcs and their angles, If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

In this case, the ARC is AB, and the angle is CBA.

CBA = 3x+32

AB = 10x+20

And,

[tex]CBA = \frac{1}{2} AB[/tex]

Now,

[tex]3x+32=\frac{1}{2} (10x+20)[/tex]

[tex]3x+32=5x+10\\32=2x+10\\22=2x\\11=x[/tex]

Now we can substitute x into the equation that equals AB

[tex]10(11)+20 \\=110+20\\=130[/tex]

So, the answer is 130, sorry I took a while, the explanation takes a long time to do lol.

Have a nice day fam. Spread The Love.

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