Angles in the same segment 40 and x

Step by step

The question

Question: find x.

C and D are on the same side of AB.

The angles at C and D are 40° and x.

1 Use the circle rule

The line AB cuts the circle into two parts, called segments.

C and D are in the same part.

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

Look at the angle at the center on that arc.

The circle rule says it is double each of them.

Both angles are half of the same angle.

So they are equal.

So the two angles are equal: x = 40.