Step by step
The question
Question: what is the exterior angle, if a triangle has inside angles 40° and 75°?
We push the bottom side out past the right corner.
The angle outside, between the push-out and the triangle, is the exterior angle.
1 Third inside angle
The angles inside a triangle add up to 180°.
180 minus 40 minus 75 is 65°.
Careful!
65° is the inside angle at that corner.
The outside angle is next to it, on the straight line.
2 Angles on a line
The inside angle and the outside angle make a straight line: 180°.
180 minus 65 is 115°.
3 The rule
Look: 40 plus 75 is 115, the same as the outside angle.
The exterior angle is the two far inside angles added together.
This is always true.
4 Check
Let's check: the triangle's angles, 40 plus 75 plus 65, make 180.
And on the line, 65 plus 115 makes 180.
So the answer is right!
Let's look back.
First: third inside angle.
Then: angles on a line.
Then: the rule.
Last: check.