Mathematics Simple Angle Facts

Aims of the Lesson By the end of the lesson you should… know the terms complementary and supplementary (in the context of angles) as well as vertically opposite be able to find missing angles… Within right angles On straight lines Around a point Inside triangles Inside quadrilaterals

Complementary Angles Together, complementary angles form a right angle. Therefore they add up to 90° Workings (example 1): x + 47 = 90 + 47 = 90 47 x 43 so x = 43 Workings (example 2): x + 47 = 90 90 – 47 = 43 so x = 43

In the first worked example you are asking what value added to 47 gives a total of 90. In the second worked example you are saying if I take the 47 off the 90, x will be the value that is left over. (This is the recommended method!) You can choose either of these methods or one of your that works, and when undertaking additions and subtractions you can of course use the column method. Save and complete the worksheet: AngleComp-S1.xlsx

Supplementary Angles Together, supplementary angles form a straight angle or a straight line. Therefore they add up to 180° Workings (example 1): x + 121 = 180 + 121 = 180 59 so x = 59 121 x Workings (example 2): x + 121 = 180 180 – 121 = 59 so x = 59

In the first worked example you are asking what value added to 121 gives a total of 180. In the second worked example you are saying if I take the 121 away from 180, x will be the value that is left over. (This is the recommended method!) You can choose either of these methods or one of your that works, and when undertaking additions and subtractions you can of course use the column method.

Angles around a point Together, angles round a point form a complete circle. Therefore they add up to 360° 133 x 168 Workings (example 1): x + (133 + 168) = 360 + 301 = 360 59 so x = 59 Workings (example 2): x + (133 + 168) = 360 x + 301 = 360 360 – 301 = 59 so x = 59

In the first worked example you are asking what value added to 133 and 168 (which together make 301) gives a total of 360. In the second worked example you are adding together all the known angles (133 and 168) then saying if I take the 301 off the 360, x will be the value that is left over. (This is the recommended method!) You can choose either of these methods or one of your that works, and when undertaking additions and subtractions you can of course use the column method. Save and complete the worksheet: AnglesSLP-S1.xlsx

Angles in a Triangle Together, the three angles in any triangle always add up to 180° Look out for special triangles that have lines of symmetry or contain right angles. Before starting to work out ‘x’ you should note that 2 lines are of equal length. This means that there is a line of symmetry here… This also means that the angle left blank is also 63… x 63° 63° Worked example: x + (63 + 63) = 180 x + 126 = 180 180 – 126 = 54 so x = 54

In this worked example you are adding the two angles you know (63 and 63) together. By taking their total (126) away from 180, you are finding what is left over, which is the value of the last angle, x. The example shows the addition and subtraction written in lines, but you could use column methods of you wish. Work through the MyMaths lesson and then its online homework called: Shape > Angles > Angle Sums Lesson: http://app.mymaths.co.uk/256-resource/angle-sums HW: http://app.mymaths.co.uk/256-homework/angle-sums

Angles in a Quadrilateral Together, the four angles in any 4-sided shape always add up to 360° Look out for special properties or right angles. You are told that although no properties are marked on it, this shape is a kite. You therefore know it has a line of symmetry here… ..and thus the angle left blank is actually 97°. 97° x 41° Worked example: x + (97 + 97 + 41) = 360 x + 235 = 360 360 – 235 = 125 so x = 125 97°

In this worked example you are adding the three angles you know (97, 97 and 41) together. By taking their total (235) away from 360, you are finding what is left over, which is the value of the last angle, x. The example shows the addition and subtraction written in a line, but you could use column methods of you wish. Save and complete the worksheet: AnglesTQ-S1.xlsx

Vertically Opposite Angles Whenever any two straight lines cross you get four angles. These are two pairs of vertically opposite angles. Unless the two lines cross at right angles (i.e. are perpendicular), then there will be two acute angles and two obtuse angles. Vertically opposite angles are EQUAL to each other. 1 2 4 3

What next? Print out the notes called Angle3-Simple.docx and answer the questions. Work through the MyMaths lesson called Angle Reasoning found at: http://app.mymaths.co.uk/257-resource/angle-reasoning Now move on to the Angle4 powerpoint