Question

If x,y, and z were the angles of triangle such that x=2y and y= z-20 degrees, how many degrees are there in angle x?

Answer 1

`x=80`

Explanation:

`y=z-20` so `x=2(z-20)=2z-40`

`2z-40 +z-20 +z =180`

`4z-60=180`

`4z=240`

`z=60`

`y=60-20=40`

`x=2 xx 40 = 80`

Answer 2

`x=80^@`

Explanation:

`"the 3 angles sum to "180^@`

`rArrx+y+z=180`

`rArr2y+z-20+z=180`

`"to solve we require an equation in 1 variable"`

`y=z-20rArrz=y+20`

`"expressing as an equation in y"`

`rArr2y+(y+20-20)+(y+20)=180`

`rArr4y+20=180`

`rArr4y=180-20=160`

`rArry=160/4=40`

`rArranglex=2xx40=80^@`