Angle Rules

Complementary & Supplementary Angles

Complementary anglesAdd to 90 degreesComplementary Angle diagram
Supplementary anglesAdd to 180 degreesSupplementary Angle diagram

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

Vertically Opposite Angles

Vertically opposite anglesEqualVertically Opposite Angle diagram

Angles of Parallel Lines

Corresponding angles(F shape)Corresponding Angle diagram
Co-interior anglesAdd to 180 degrees (U shape)Cointerior Angle diagram
Alternate anglesEqual (Z shape)Alternate Angle diagram

Angles of Triangles

Angle sum of triangleAdd to 180 degreesSum of Triangle diagram
Equilateral triangleAll angles equal 60 degreesEquilateral Triangle diagram
Isosceles triangleBase angles are equalIsosceles Triangle diagram
Exterior angle of triangleThe exterior angle equals the
sum of the two interior opposite angles.
Exterior Triangle diagram

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

Angle sum of quadrilateralAdd to 360 degreesAngles of Quadrilateral diagram
Opposite angles of parallelogramEqualAngles of Parallelogram diagram

Angles of Circles

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