Angle Rules


Complementary & Supplementary Angles

NAMERULEDIAGRAM
Complementary anglesAdd to 90 degreesDiagram of complementary angle
Supplementary anglesAdd to 180 degreesDiagram of supplementary angle

(Hint to remember these: C in the alphabet and 90 when counting both come before S and 180.)


Vertically Opposite Angles

NAMERULEDIAGRAM
Vertically opposite anglesEqualDiagram of vertically ppposite angle

Angles of Parallel Lines

NAMERULEDIAGRAM
Corresponding angles(F shape)Diagram of corresponding angles
Co-interior anglesAdd to 180 degrees (U shape)Diagram of cointerior angles
Alternate anglesEqual (Z shape)Diagram of alternate angle

Angles of Triangles

NAMERULEDIAGRAM
Angle sum of triangleAdd to 180 degreesDiagram of sum of a triangle
Equilateral triangleAll angles equal 60 degreesDiagram of equilateral triangle
Isosceles triangleBase angles are equalDiagram of isosceles triangle
Exterior angle of triangleThe exterior angle equals the
sum of the two interior opposite angles.
Diagram of exterior triangle

Question - Angle Sum of Triangle

To show that the angle sum of a triangle equals 180 degrees, draw a triangle, tear the angles and rearrange them into a straight line. Remember that the number of degrees in a straight line is 180 degrees.

Do a similar activity to show that the angles of a quadrilateral add to 360 degrees.

Angles of Quadrilaterals

NAMERULEDIAGRAM
Angle sum of quadrilateralAdd to 360 degreesDiagram of quadrilateral angles
Opposite angles of parallelogramEqualDiagram of parallelogram angles

Angles of Circles

NAMERULEDIAGRAM
Radius meets tangentThe radius meets the tangent at right angles. Diagram of radius and tangent
Angle at centreThe angle subtended at the centre of the circle is twice the angle at the circumference.
(arrow shape)
Diagram of angle at centre
Angle at circumferenceAngles subtended by the same chord are equal.
(butterfly shape)
Diagram of angle at circumference
Opposite angles of cyclic quadrilateralEqual Diagram of opposite quadrilateral
Exterior angle of cyclic quadrilateralThe exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. Diagram of exterior quadrilateral