Question

PLA ANSWER I DONT KNOW THIS

Answer 1

x=45

Explanation:

I can give you two solutions

First solution:

In
`\triangle FBA` we know that

`\angle BFA + \angle FAB + \angle ABF=180\\\\90+x+\angle ABF =180\\\\\angle ABF =90-x`

same case for
`\angle EBC` in
`\triangle ECB`

so we have that

`\angle ABC = \angle ABF + \angle FBE +\angle EBC\\\\\angle ABC = 90-x+45+90-x\\\\\angle ABC = 180+45-2x`

we leave it like that because it's convenient

Now by properties of parallelograms we know that opposite sides add up to 180

`\angle FAB + \angle ABC = 180\\\\x+180+45-2x=180\\\\x+45-2x=0\\\\45-x=0\\\\x=45`

so one angle is 45 and the other one is 135

Solution 2

if we look at DEBF we can say that it's a cyclic quadrilateral

because opposite sides add up to 180

in our case

`\angle DFB = 180 -\angle BFA = 180-90 = 90\\\\\angle DEB = 90\\\\\Rightarrow \angle DFB + \angle DEB = 180\\\\`

so for the other to angles is also true

`\angle FDE + \angle EBF = 180\\\\\angle FDE +45 = 180\\\\\angle FDE = 135`

so that's the measure of one angle of the parallelogram

the other angle x is

`\angle EDF + \angle FAB = 180\\\\135+x=180\\\\x=45`

There you go choose yourself