Exterior angle of a triangle, inside angles 35 and 90

Step by step

The question

Question: what is the exterior angle, if a triangle has inside angles 35° and 90°?

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 35 minus 90 is 55°.

Careful!

55° 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 55 is 125°.

3 The rule

Look: 35 plus 90 is 125, 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, 35 plus 90 plus 55, make 180.

And on the line, 55 plus 125 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.