Opposite Angles in Cyclic Quadrilaterals

The opposite angles of a cyclic quadrilateral sum to 180°.

Tangent Perpendicular to the Radius

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

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.

Angles at the center of a circle

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

• The sum of the exterior angles of a hexagon is 360°.
• The sum of the interior angles of a hexagon is 720°.
• The angles at a point sum to 360°.

Interior/Exterior angle of a Quadrilateral

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

Angles and parallel angles.

• 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°.

Exterior angles of a triangle

The exterior angle of a triangle the sum of its interior opposite angles.

Angle sum of a triangle.

• The angle sum of a triangle is 180°.

Angles in a line.

• If two angles sum to 180 º they are called supplementary angles.
• When two lines intersect, the vertically opposite angles are equal.
• The angle sum of a straight line is 180º.