Question

Trapezoid STUV shown below is an isosceles trapezoid. Use this to solve for x and y.

Answer 1

Given that the figure is an isosceles trapezoid,

Isosceles trapezoid is a trapezoid whose two opposite sides and two adjacent angles are congruent.

Therefore,

`\begin{gathered} 14x-25=19y+10 \\ 14x-19y=10+25 \\ 14x-19y=35\ldots\ldots\ldots.1 \end{gathered}`

Also,

`\begin{gathered} \angle U+\angle T=180 \\ 3x+1+19y_{}+10=180 \\ 3x+19y+11=180 \\ 3x+19y=180-11 \\ 3x_{}+19y=169\ldots\ldots\ldots\ldots.2 \end{gathered}`

Combining the two equations together and solving for x and y

`\begin{gathered} 14x-19y=35\ldots\ldots\ldots.1 \\ 3x_{}+19y=169\ldots\ldots\ldots\ldots.2 \end{gathered}`

Isolate x from equation 1

`\begin{gathered} 14x=35_{}+19y \\ \therefore x=(35+19y)/(14) \end{gathered}`
`\begin{gathered} \mathrm{Substitute\: }x=(35+19y)/(14)\text{ into equation 2} \\ 3*(35+19y)/(14)+19y=169 \\ (105+323y)/(14)=169 \end{gathered}`

Solve for y

`\begin{gathered} 105+323y=169*14 \\ 323y=169*14-105 \\ 323y=2261 \\ y=(2261)/(323)=7 \\ \therefore y=7 \end{gathered}`
`\begin{gathered} \mathrm{For\: }x=(35+19y)/(14) \\ \mathrm{Substitute\: }y=7 \\ x=(35+19*7)/(14)=(35+133)/(14)=(168)/(14)=12 \\ \therefore x=12 \end{gathered}`

Hence,

`x=12,y=7`