Question

Why is the exterior angle of a triangle equal to the sum of the two remote interior angles?

Answer 1

I can't see the whole drawing,,, @agostino

Answer 2

In words,

consider a triangle with angles a, b, c.

Say we extend a side of the triangle such that there is another angle d which satisfies d=180-c, i.e. an exterior angle of the triangle.

We have a+b+c=180 and by c+d=180, we have a+b=d.

Answer 3

\[A+B+C=180\]PROPERTY OF TRIANGLE SUM\[D=180-C\]SUPPLEMENTARY ANGLES\[NOW C=180-D \]

Answer 4

SUBSTITUTE IT INTO THE 1ST EQUATION

Answer 5

A+B+(180-D)=180
A+B+180-D=180
A+B=D

Answer 6

thanks guys!

Answer 7

HENCE PROVED!!