Question

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

Answer 1

Answer:

Part 1) $x=28.75\°$

Part 2) $z=44.5\°$

Part 3) $y=135.5\°$

Step-by-step explanation:

Part 1) Determine the value of x

we know that

$(\frac{6}{5}x+10)\°=(2x-13)\°$ ------> by corresponding angles

Solve for x

Multiply by 5 both sides to remove the fraction

$5(\frac{6}{5}x+10)\°=5(2x-13)\°$

$6x+50=10x-65$

$10x-6x=50+65$

$4x=115$

Divide by 4 both sides

$x=28.75\°$

Part 2) Determine the value of z

we know that

$z=(\frac{6}{5}x+10)\°$ ------> by corresponding angles

we have

$x=28.75\°$

substitute the value of x and solve for z

$z=(\frac{6}{5}(28.75)+10)=44.5\°$

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

$y+44.5\°=180\°$

$y=180\°-44.5\°=135.5\°$