In circle ZZ, m, arc, X, Y, equals, 143, degreesm

Question

XY
⌢
=143
∘
. Solve for xx if m, angle, X, Z, Y, equals, left bracket, 9, x, plus, 30, right bracket, degreesm∠XZY=(9x+30)
∘
. If necessary, round your answer to the nearest tenth.

Answer 1

Since arc XY is 143 degrees, we know that m∠XZY = 1/2 * m(arc XY) = 1/2 * 143 = 71.5 degrees.

Now we can set up the equation:
9x + 30 = 71.5

Subtract 30 from both sides:
9x = 41.5

Divide by 9:
x = 41.5/9 = 4.61

So x is approximately 4.6.