Question

How would you solve this I’m confused

Answer 1

`x=8.5^o`

Explanation:

Notice that since segments AB and DE are parallel, then angles
`\angle A` and
`\angle E` must be equal since they are alternate angles in between parallel lines.

So,
`\angle E = 50^o`. We also know that
`\angle C = 45^o`, then the remaining angle (
`\angle D`) in triangle CDE must be such that added to the other two angles results in
`180^o`. That is:

`\angle D = 180^o-\angle C-\angle E\\\angle D = 180^o-45^o-50^o\\\angle D= 85^o`

Now, since angle D equals 10 times x, we can solve for the unknown x in the equation:

`\angle D=10\,x\\85^o=10\,x\\x=(85^o)/(10)\\\\x=8.5^o`