Question

Tanya wants to test the theory that the exterior angles of a

Answer 1

Answer:

$f + e + d = 360^o$

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:

$a + f = 180$

$b + e = 180$

$c + d = 180$

Make f, e and d the subject

$f = 180 - a$

$e = 180 - b$

$d = 180 - c$

Add up the equations

$f + e + d = 180 -a + 180 - b + 180- c$

Collect like terms

$f + e + d = 180 + 180+ 180-a- b - c$

$f + e + d = 540-a- b - c$

We have:

$f + e + d = 540-(a+ b + c)$

$a + b + c \to 180$ --- angles in a triangle

So, we have:

$f + e + d = 540-180$

$f + e + d = 360^o$ --- proved