Properties of Shape - Angles in Regular Polygons - Worksheet

In Lesson 12 of the Geometry series, students delve into the world of regular polygons, focusing on understanding and calculating their interior angles. The National Curriculum objective is to recognise angles at a point, on a straight line, or when they are vertically opposite, and to find missing angles. To facilitate learning, differentiated worksheets and teaching slides are provided as resources. Students will familiarise themselves with key terms such as angle, parallelogram, rhombus, trapezium, quadrilateral, interior angles, polygons, partition, vertex, and exterior angle. The lesson aims to empower students to apply their knowledge of shapes to partition polygons from a single vertex into triangles, which helps in determining the sum of the angles within the polygons. They will also use the rule that angles on a straight line add up to 180° to calculate exterior angles.

Throughout the lesson, students are encouraged to engage with critical questions, such as defining regular and irregular polygons, recalling the sum of interior angles of a triangle, and utilising this information to deduce the interior angles of various polygons. They will also look for patterns and make predictions about the angle sums of other polygons. The activities involve filling in a table by partitioning shapes such as rectangles, quadrilaterals, and pentagons into triangles and using the formula (number of triangles x 180°) to find the sum of internal angles for each shape. For instance, a quadrilateral is partitioned into two triangles, leading to a sum of internal angles of 360°. The lesson progresses to problem-solving tasks where students use given clues to determine the shapes being described and their interior angle sums, enhancing their reasoning skills in the context of geometry.