Question

Any answers for these two questions?

Answer 1

`\large\textsf{Answer:}`

`\mathtt{x = 9.4}`

`\mathtt{y = 14.3}`

`\textsf{Please see below.}`

`\large\textsf{Step-by-step explanation:}`

`\textsf{For these problems, we are asked to solve for the missing variables.}`

`\textsf{To start, we have \underline{2 exterior angles} and \underline{2 secant lines }that \underline{intersect} at a \underline{vertex}.}`

`\boxed{\Large\textsf{What is a Vertex?}}`

`\textsf{A \underline{Vertex} is a \underline{point of intersection} of \underline{2} or more \underline{lines.}}`

`\boxed{\Large\textsf{What are Exterior Angles?}}`

`\textsf{\underline{Exterior Angles} are \underline{angles} that are \underline{outside} of a circle.}`

`\boxed{\Large\textsf{What are Secant Lines?}}`

`\textsf{\underline{Secent Lines} are \underline{lines} that intersect a circle \underline{twice}.}`

`\textsf{Because we have Intersecting Secants \underline{outside} of the circle, we should use this formula;}`

`\mathtt{a(a+b)=c(c+d)}\\`

`\textsf{Smaller segment is first, then the larger segment is inside the parentheses.}`

`\underline{\textsf{Substitute values from 10;}}`

`\mathtt{5(5+x)=6(6+6)}`

`\underline{\textsf{Multiply:}}`

`\mathtt{25+5x = 72}`

`\underline{\textsf{Subtract 25 from both sides:}}`

`\mathtt{5x = 47}`

`\underline{\textsf{Divide by 5:}}`

`\boxed{\mathtt{x = 9.4}}`

`\textsf{Let's do the same for 11.}`

`\underline{\textsf{Substitute values from 11;}}`

`\mathtt{10(10+y)=9(9+18)}`

`\underline{\textsf{Multiply:}}`

`\mathtt{100+10y=243}`

`\underline{\textsf{Subtract 100 from both sides:}}`

`\mathtt{10y=143}`

`\underline{\textsf{Divide by 10:}}`

`\boxed{\mathtt{y=14.3}}`