Question

find the value or measure. Assume all lines that appear to be tangent are tangent.

Answer 1

Given :

m SW = 12x - 5

m TV = 2x + 7

m∠ TUV = 6x - 19

so,

m∠ TUV = 0.5 * ( m SW - m TV)

so,

$6x-19=\frac{1}{2}\lbrack(12x-5)-(2x+7)\rbrack$

Solve for x;

$\begin{gathered} 12x-38=12x-5-2x-7 \\ 12x-38=10x-12 \\ 12x-10x=38-12 \\ 2x=26 \\ \\ x=\frac{26}{2}=13 \end{gathered}$

so, the measure of the arc SW = 12x - 5 = 12 * 13 - 5 = 151