Angle sums and regular polygons.
15 original questions, 53 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A hexagon has 6 sides.
Each exterior angle of a regular polygon is 30°.
Work out the number of sides of the polygon.
Work out the size of each interior angle of a regular decagon.
Five of the exterior angles of a hexagon are 40°, 50°, 60°, 70° and 80°.
Work out the size of the sixth exterior angle.
Each interior angle of a regular polygon is 156°.
Work out the number of sides of the polygon.
In a regular polygon, each interior angle is 100° more than each exterior angle.
Work out the number of sides of the polygon.
The interior angles of a pentagon are x°, (x + 30)°, (x + 40)°, 2x° and (2x + 50)°.
Work out the size of the largest interior angle of the pentagon.
Each exterior angle of a regular polygon is 18°.
In a pentagon, four of the interior angles are equal.
The fifth interior angle is 60° larger than each of the equal angles.
Work out the size of the largest interior angle of the pentagon.
ABCDEF is a hexagon.
Angle A = angle D = 90°.
The other four interior angles are all equal.
Work out the size of angle B.
A regular pentagon and a square have the same side length.
They are joined along one common edge PQ, on opposite sides of PQ, so they do not overlap.
At the vertex P, the pentagon has an interior angle and the square has an interior angle.
Work out the size of the angle at P that is outside both the pentagon and the square.
The sum of the interior angles of a polygon is 1800°.
ABCDE is a regular pentagon.
The diagonal AC is drawn.
Work out the size of angle ACD.
Give a reason for each stage of your working.
In a regular polygon, the ratio of each interior angle to each exterior angle is 13 : 2.
Regular pentagon ABCDE and regular hexagon ABFGHI have the same side length.
They share the common edge AB and lie on opposite sides of AB, so they do not overlap.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.