Question

Determine the value of each variable. Enter your answers as decimals.
X:
Y:
Z:

Answer 1

Part 1)
`x=28.75\°`

Part 2)
`z=44.5\°`

Part 3)
`y=135.5\°`

Explanation:

Part 1) Determine the value of x

we know that

`((6)/(5)x+10)\°=(2x-13)\°` ------> by corresponding angles

Solve for x

Multiply by 5 both sides to remove the fraction

`5((6)/(5)x+10)\°=5(2x-13)\°`

`6x+50=10x-65`

`10x-6x=50+65`

`4x=115`

Divide by 4 both sides

`x=28.75\°`

Part 2) Determine the value of z

we know that

`z=((6)/(5)x+10)\°` ------> by corresponding angles

we have

`x=28.75\°`

substitute the value of x and solve for z

`z=((6)/(5)(28.75)+10)=44.5\°`

Part 3) Determine the value of y

we know that

`y+z=180\°` ------> by supplementary angles

we have

`z=44.5\°`

substitute and solve for y

`y+44.5\°=180\°`

`y=180\°-44.5\°=135.5\°`