Angle at the center 130, angle at the edge x

Step by step

The question

Question: find x.

The angle at the center is 130°.

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 = 130/2.

130 divided by 2 is 65.

So x = 65.

2 Check

Let's check: double 65°.

130° is double 65°.

So x = 65 is right!

Let's look back.

First: use the circle rule.

Last: check.