Another example of translating English sentences to mathematical sentences comes from geometry. A well known property of triangles is that all three angles will always add to 180. For example, the first angle may be 50 degrees, the second 30 degrees, and the third 100 degrees. If you add these together, 50 + 30 + 100 = 180. We can use this property to find angles of triangles. Example The second angle of a triangle is double the first. The third angle is 40 less than the first. Find the three angles.

`x`	Set First Angle `x`
`2x`	The second is double the first,
`x-40`	The third is 40 less than the first
`(x)+(2x)+(x−40)=180`	All three angles add to 180
`x+2x+x−40=180`
`4x−40=180`
`4x−40color(red)(-40)=180color(red)(-40)`
`4x=220`
`(4x)/color(red)(4)=220/color(red)(4)`
`x=55 `

First Angle `= 55` Second Angle `= 2(55) = 110` Third Angle `=55-40=15` Another geometry problem involves perimeter or the distance around an object. For example, consider a rectangle has a length of 8 and a width of 3. There are two lengths and two widths in a rectangle (opposite sides) so we add `8 + 8 + 3 + 3 = 22`. As there are two lengths and two widths in a rectangle an alternative to find the perimeter of a rectangle is to use the formula `P = 2L + 2W` . So for the rectangle of length 8 and width 3 the formula would give, `P = 2(8) + 2(3) = 16 + 6 = 22`. With problems that we will consider here the formula `P = 2L + 2W` will be used. Example The perimeter of a rectangle is 44. The length is 5 less than double the width. Find the dimensions.

`x`	Make the length `x`
`2x−5 `	Width is five less than two times the length
`P =2L+2W `	The formula for perimeter of a rectangle
`(44)=2(x)+2(2x−5)`	Replace P , L, and W with labeled values
`44=2x+4x−10 `	Distribute through parenthesis
`44=6x−10`	Combineliketerms
`44color(red)(+10)=6x−10color(red)(+10)`
`54=6x `
`54/color(red)(6)=(6x)/color(red)(6)`
`9=x`

Length: `=9` Width: `=2(9)-5 =13`