Angle at the center x, angle at the edge 52

Step by step

The question

Question: find x.

The angle at the center is x.

The angle at the edge is 52°.

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 52: x = 2 × 52.

2 times 52 is 104.

So x = 104.

2 Check

Let's check: double 52°.

104° is double 52°.

So x = 104 is right!

Let's look back.

First: use the circle rule.

Last: check.