Question

m∠WYX = (4x − 8)° and m∠WYZ = 10x°. If ∠WYX and ∠WYZ are complementary, find the measure of each angle.

Answer 1

The answers would be:
WYX = 20 degrees
WYZ = 70 degrees

Answer 2

`m\angle WYX=20^(\circ)`

`m\angle WYZ=70^(\circ)`

Explanation:

We have been given that
`m\angle WYX=(4x-8)^(\circ)` and
`m\angle WYZ=(10x)^(\circ)`.

Since ∠WYX and ∠WYZ are complementary, so they will add up-to 90 degrees.

`m\angle WYZ+m\angle WYX=90^(\circ)`

Substitute the given values:

`4x-8+10x=90`

Combine like terms:

`14x-8=90`

`14x-8+8=90+8`

`14x=98`

`(14x)/(14)=(98)/(14)`

`x=7`

Let us substitute
`x=7` in measure of each angle as:

`m\angle WYX=(4(7)-8)^(\circ)`

`m\angle WYX=(28-8)^(\circ)`

`m\angle WYX=20^(\circ)`

Therefore, the measure of angle WYX is 20 degrees.

`m\angle WYZ=(10x)^(\circ)`

`m\angle WYZ=(10(7))^(\circ)`

`m\angle WYZ=70^(\circ)`

Therefore, the measure of angle WYZ is 70 degrees.