Today Your Knowledge of How to Find Angles Around a Point, in Triangles

L.O – To know how to calculate missing polygon angles 1.4.20

Key vocabulary: congruent (of equal length), quadrilateral, angles, parallel, perpendicular, opposite, equal, adjacent (joining next to), polygons, properties, triangles, quadrilaterals, pentagon, hexagon, heptagon, octagon, nonagon, decagon, interior, exterior.

Hello Year 6!!

Today your knowledge of how to find angles around a point, in triangles, in quadrilaterals, and the fact that vertically opposite angles are equal will be very useful in your understanding of identifying angles in a range of polygons.

Please complete SECTION A or B depending on how confident you are feeling. All these activities do not need to be printed out unless you prefer to.

Read this first - Key Facts Before You Start Your Studies What is a polygon? A polygon is any closed 2d shape with sides that are all straight. So far you have studied triangles and quadrilaterals but what about shapes with 5 or more sides and angles?

What are regular and irregular polygons?

SECTION A

Task 1 Find a piece of paper. Draw any quadrilateral e.g. a square, rhombus, rectangle. Then partition it into 2 triangles marking them A and B. What do the interior angles of triangle A add up to? What do the interior angles of triangle B add up to? So what is the sum of all the angles in a triangle? Answer = 180 + 180 = 360 degrees (or 180 x 2 = 360 degrees).

This information has been included in the table below. Can you look for patterns in the table and fill in the missing information. Either copy this table onto paper or print it out. ______

Shape Number of Number of 180 x (times) Sum of all the sides triangles the number interior angles of triangles equals of the shape

Triangle 3 1 180° x 1 180° Quadrilateral 4 2 180° x 2 360° Pentagon 5 3 = Hexagon 6 180° x 4 Heptagon 900° Octagon 6 Nonagon 9 180° x 7 Decagon 1440° The information in this table can be used to help you solve today’s problems. What do you notice about the number of sides compared to the number of triangles? ______

Task 2 Task 3 (a) Draw a pentagon with 3 right angles.

(b) What is the size of angle ‘a’ ? Show your method.

Section A (cont) Task 4 (a)Which of these shapes are octagons? (b)Which 2 shapes have at least 1 right-angle?

Extension challenge Use the table in Task 1 to help you What are the sizes of interior angles A and B?

Optional: Have a go at different questions in Section B 3

SECTION B Task 1 Find a piece of paper. Draw any quadrilateral e.g. a square, rhombus, rectangle. Then partition it into 2 triangles marking them A and B. What do the interior angles of triangle A add up to? What do the interior angles of triangle B add up to? So what is the sum of all the angles in a triangle? Answer = 180 + 180 = 360 degrees (or 180 x 2 = 360 degrees).

This information has been included in the table below. Can you look for patterns in the table and fill in the missing information. Either copy this table onto paper or print it out. ______

Shape Number Number 180 x (times) Total of all the Size of one of of of the number interior angles the interior sides triangles of triangles equals of the shape angles

Triangle 180° x 1 180° 60 Quadrilateral 4 2 180° x 2 360° 90 Pentagon 5 3 = Hexagon Heptagon Octagon Nonagon Decagon The information in this table can be used to help you solve today’s problems. ______Task 2 What do you notice in the table from Task 1? What is the relationship between the number of sides and the number of triangles? Can you predict the sum of any other polygons?

(a) Can you find the sum of all the interior angles of a tetradecagon (14 sided polygon)? (b) How many triangles can be created in a polygon with 101 sides? (c) What is the total sum of all the interior angles in a hectagon (100 sided polygon) ?

Task 3 Task 4 Draw a pentagon that has 3 right angles on this sheet or in your maths book.

Use the information from the table and your knowledge of finding angles to find the size of angle ‘a’.

Section B (cont) Task 5

Extension activity for those who like a real challenge!