Exterior angle of a triangle, inside angles 50 and 60 Easy

The question

Question: what is the exterior angle, if a triangle has inside angles 50° and 60°?

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 50 minus 60 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: 50 plus 60 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, 50 plus 60 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.

▶ Watch it solved

Exterior angle 120, inside angles 70 and x Medium

The question

Question: if the exterior angle is 120° and the far inside angles are 70° and x°, what is x?

The exterior angle is outside the triangle, on the pushed-out side.

1 Use the rule

The exterior angle is the two far inside angles added together.

So 70 + x = 120.

Careful!

The outside angle is not inside the triangle.

It does not go in the 180° sum.

2 Remove the 70

We want x by itself.

The 70 is in the way.

To remove 70, we take away 70.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

70 and − 70 make zero.

Cross them out.

120 − 70 = 50.

So x = 50!

3 Check

Let's check: with x = 50, the inside angles are 70° and 50°.

Together 120°, the outside angle.

So the answer is right!

Let's look back.

First: use the rule.

Then: remove the 70.

Last: check.

▶ Watch it solved

Exterior angle 3x + 10, inside angles x and 50 Harder

The question

Question: if the exterior angle is (3x + 10)° and the far inside angles are x° and 50°, what is x?

The exterior angle is outside the triangle, on the pushed-out side.

1 Use the rule

The exterior angle is the two far inside angles added together.

So x + 50 = 3x + 10.

Careful!

The outside angle is not inside the triangle.

It does not go in the 180° sum.

2 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the x from the left side.

To remove x, we take away x.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

x and − x make zero.

Cross them out.

3x − x = 2x.

Now we have 50 = 2x + 10.

Let's swap the two sides, so x is on the left.

We want x by itself.

Two things are stuck to x: times 2 and + 10.

The + 10 is on the outside, so it comes off first.

Then the times 2.

3 Remove the + 10

To remove + 10, we take away 10.

We do it on both sides, so they stay equal.

+ 10 and − 10 make zero.

Cross them out.

50 − 10 = 40.

Now we have 2x = 40.

4 Remove the 2

2x means 2 times x.

We want just x.

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 divided by 2 is 1.

So just x is left.

40 divided by 2 is 20.

So x = 20!

5 Check

Let's check: with x = 20, the inside angles are 20° and 50°.

Together 70°, the outside angle.

So the answer is right!

Let's look back.

First: use the rule.

Then: get x on one side.

Then: remove the + 10.

Then: remove the 2.

Last: check.

▶ Watch it solved