Question

10.

Consider the figure below.
(502 +13)
(45x+)
(44x + 125y)
(802 - 14)
The angle measures are represented by algebraic expressions. Determine the
values of x, y, and z.

Answer 1

Part 1) The value of y is
`y=0.8`

Part 2) The value of z is
`z=0.9`

Part 3) The value of x is
`x=0.5`

Explanation:

step 1

Find the value of y

we know that

`((225y)/(2))\°=90\°` ----> given problem (is a right angle)

`y=90(2)/225`

`y=0.8`

step 2

Find the value of z

we know that

`(50z+13)\°=(80z-14)\°` ----> by vertical angles

Solve for z

`80z-50z=13+14`

`30z=27`

`z=27/30`

`z=0.9`

step 3

Find the value of x

we know that

`(44x+125y)\°+(80z-14)\°=180\°` ----> by supplementary angles (linear pair)

Substitute the value of y and the value of z and solve for x

`(44x+125(0.8))\°+(80(0.9)-14)\°=180\°`

`(44x+100)\°+(72-14)\°=180\°`

`44x+158=180`

`44x=180-158`

`44x=22`

`x=0.5`