Question

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

triangle add up to 360°. She draws triangle ABC and finds all

the angles in the triangle.

PLEASE HELP!!

Answer 1

`f + e + d = 360^o`

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