Answer:
[tex]f + e + d = 360^o[/tex]
Step-by-step explanation:
The question is incomplete, as what is required is not stated and the triangle is not given.
So, I will solve generally.
The proof is as follows (see attachment for triangle)
From the attachment, we have:
[tex]a + f = 180[/tex]
[tex]b + e = 180[/tex]
[tex]c + d = 180[/tex]
Make f, e and d the subject
[tex]f = 180 - a[/tex]
[tex]e = 180 - b[/tex]
[tex]d = 180 - c[/tex]
Add up the equations
[tex]f + e + d = 180 -a + 180 - b + 180- c[/tex]
Collect like terms
[tex]f + e + d = 180 + 180+ 180-a- b - c[/tex]
[tex]f + e + d = 540-a- b - c[/tex]
We have:
[tex]f + e + d = 540-(a+ b + c)[/tex]
[tex]a + b + c \to 180[/tex] --- angles in a triangle
So, we have:
[tex]f + e + d = 540-180[/tex]
[tex]f + e + d = 360^o[/tex] --- proved
