Angle at the center 80, angle at the edge x

Step by step

The question

Question: find x.

The angle at the center is 80°.

The angle at the edge is x.

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 the angle at the edge is half of the angle at the center: x = 80/2.

80 divided by 2 is 40.

So x = 40.

2 Check

Let's check: double 40°.

80° is double 40°.

So x = 40 is right!

Let's look back.

First: use the circle rule.

Last: check.