Step by step
The question
Question: what is the exterior angle, if a triangle has inside angles 80° and 30°?
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 80 minus 30 is 70°.
Careful!
70° 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 70 is 110°.
3 The rule
Look: 80 plus 30 is 110, 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, 80 plus 30 plus 70, make 180.
And on the line, 70 plus 110 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.