Angle at the center x, angle at the edge 35 Easy

The question

Question: find x.

The angle at the center is x.

The angle at the edge is 35°.

1 Use the circle rule

O is the center of the circle.

Lines from A and B to the center make the angle at the center.

Lines from A and B to C, on the edge, make the angle at the edge.

Both angles stand on the same arc: the orange part of the circle, from A to B.

Circle rule: the angle at the center is double the angle at the edge.

This is always true.

So x is double 35: x = 2 × 35.

2 times 35 is 70.

So x = 70.

2 Check

Let's check: double 35°.

70° is double 35°.

So x = 70 is right!

Let's look back.

First: use the circle rule.

Last: check.

▶ Watch it solved

Angle at the edge 48, angle at the center x Medium

The question

Question: find x.

The angle at the center is x.

The angle at the edge is 48°.

1 Use the circle rule

O is the center of the circle.

Lines from A and B to the center make the angle at the center.

Lines from A and B to C, on the edge, make the angle at the edge.

Both angles stand on the same arc: the orange part of the circle, from A to B.

Circle rule: the angle at the center is double the angle at the edge.

This is always true.

So x is double 48: x = 2 × 48.

2 times 48 is 96.

So x = 96.

2 Check

Let's check: double 48°.

96° is double 48°.

So x = 96 is right!

Let's look back.

First: use the circle rule.

Last: check.

▶ Watch it solved

Angle at the center 3x + 10, angle at the edge x + 25 Harder

The question

Question: find x.

The angle at the center is 3x + 10.

The angle at the edge is x + 25.

1 Use the circle rule

O is the center of the circle.

Lines from A and B to the center make the angle at the center.

Lines from A and B to C, on the edge, make the angle at the edge.

Both angles stand on the same arc: the orange part of the circle, from A to B.

Circle rule: the angle at the center is double the angle at the edge.

This is always true.

So 3x + 10 is double x + 25: 3x + 10 = 2(x + 25).

2 Open the brackets

The 2 in front of the bracket multiplies every part inside.

So we write 2 times each part.

Work out each multiplication.

3 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the 2x from the right side.

To remove 2x, we take away 2x.

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.

2x and − 2x make zero.

Cross them out.

3x − 2x = x.

Now we have x + 10 = 50.

4 Remove the + 10

We want x by itself.

The + 10 is in the way.

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.

So x = 40!

5 Check

Let's check: put x = 40 in each angle.

Now double the angle at the edge.

130° is double 65°.

So x = 40 is right!

Let's look back.

First: use the circle rule.

Then: open the brackets.

Then: get x on one side.

Then: remove the + 10.

Last: check.

▶ Watch it solved