IGCSE Maths Geometry & polygons topical questions

Find the missing angles, giving a reason each time.

1. (a)Two angles on a straight line are 118° and x. Find x.[1]
2. (b)Angles of 140°, 90° and y sit around a point. Find y.[2]

A triangle has interior angles 3x, 2x and x.

1. (a)Write down an equation for x.[1]
2. (b)Solve the equation.[1]
3. (c)Find the largest angle of the triangle.[1]
4. (d)State the type of triangle.[1]

A transversal crosses two parallel lines. One angle is 72°.

1. (a)Write down its corresponding partner.[1]
2. (b)Write down its alternate partner.[1]
3. (c)Find its co-interior partner, giving a reason.[2]

A transversal crosses two parallel lines. On the first line, the angles on one side of the transversal are x and 118° (angles on a straight line). At the second line, y is the corresponding angle to x.

1. (a)Find x.[2]
2. (b)Write down y, with a reason.[2]
3. (c)State the size of the co-interior partner of the 118° angle.[1]

A regular decagon has 10 sides.

1. (a)Write down the exterior angle.[1]
2. (b)Write down the interior angle.[1]
3. (c)Find the interior angle sum of a decagon.[2]
4. (d)Write down the number of lines of symmetry.[1]

A pentagon has interior angles 100°, 110°, 120° and 105°.

1. (a)Find the sum of the interior angles of a pentagon.[2]
2. (b)Find the fifth angle.[2]
3. (c)Write down the interior angle of a regular pentagon.[1]

A ship sails from port on a bearing of 090° for 30 km, then on a bearing of 180° for 40 km. (Extended)

1. (a)State the size of the angle between the two legs of the journey.[1]
2. (b)Find the distance of the ship from the port.[2]
3. (c)Find the bearing of the port from the ship, to 1 decimal place.[2]

A small triangle has sides 3 cm, 5 cm and 6 cm. A similar triangle has longest side 18 cm. (Extended)

1. (a)Find the scale factor.[1]
2. (b)Find the other two sides of the large triangle.[1]
3. (c)The small triangle has area 6 cm². Find the area of the large triangle.[2]

In triangle PQR, PQ = PR and the base angle at R is 65°. The side QR is extended beyond R to a point S.

1. (a)Find angle QPR.[2]
2. (b)Find the exterior angle PRS.[2]
3. (c)Write down the reason that angle PQR is also 65°.[1]

Two rectangular gardens are similar. The smaller measures 8 m by 5 m; the larger has length 20 m.

1. (a)Find the length scale factor.[1]
2. (b)Find the width of the larger garden.[1]
3. (c)Find the area of the larger garden.[2]
4. (d)Write down the area scale factor.[1]

A regular polygon has exterior angle 20°. (Extended)

1. (a)Find the number of sides.[1]
2. (b)Find the interior angle.[1]
3. (c)Find the sum of the interior angles.[2]
4. (d)State the order of rotational symmetry.[1]

In triangle ABC, angle A = 58°. The side BC is extended past C to a point D, and angle ACD = 121°.

1. (a)Find angle ACB, giving your reason.[2]
2. (b)Find angle B, giving your reason.[2]
3. (c)Verify your answers using the exterior-angle fact.[2]

The interior angles of a pentagon are x, 2x, 3x, 4x and 120°.

1. (a)Form an equation in x.[2]
2. (b)Solve the equation.[2]
3. (c)Find the largest angle of the pentagon.[1]

A plane flies from airport A on a bearing of 040° for 200 km to B, then from B on a bearing of 130° for 150 km to C. (Extended)

1. (a)Explain why angle ABC is 90°.[3]
2. (b)Find the distance AC.[2]
3. (c)Find the bearing of C from A, correct to 1 decimal place.[2]