The Angle at the Centre of a Circle

The angle at the centre of a circle is twice the angle at the circumference standing on the same arc.

Opposite Angles In Cyclic Quadrilaterals

The opposite angles of a cyclic quadrilateral sum to 180°

Angles on the Same Arc

Angles at the circumference standing on the same arc are equal.

The Angle in a Semi-Circle

The angle in a semi-circle is a right angle

Tangent Perpendicular to Radius

A tangent to a circle meets the radius at 90° at the point of contact.

INTERIOR / EXTERIOR ANGLE SUM OF A QUADRILATERAL

• The interior angle sum of a quadrilateral is 360°.
• The exterior angle sum of a quadrilateral is 360°.

Angles and Parallel Lines

• When a pair of parallel lines are cut by a transversal:

1) the corresponding angles are equal,

2) the alternate angles are equal,

3) the co-interior angles are supplementary.

• Supplementary angles are angles which sum to 180°.