Angles and Shape
Angles and shape questions test knowledge of angle facts, such as angles on a straight line, angles around a point, angles in triangles and quadrilaterals, and angles formed by parallel lines. They also cover properties of 2D shapes and polygons, including the number of sides, symmetry and the relationship between exterior and interior angles, which regularly appear in 11+ maths papers.
Method
- Learn the key angle facts: angles on a straight line add up to 180 degrees, angles around a point add up to 360 degrees, and vertically opposite angles are equal.
- Learn the angle sum rules for shapes: angles in a triangle add up to 180 degrees, and angles in a quadrilateral add up to 360 degrees.
- For parallel lines cut by a transversal, use alternate angles (equal, forming a 'Z' shape), corresponding angles (equal, forming an 'F' shape) and co-interior angles (sum to 180 degrees, forming a 'C' shape).
- For polygons, use the fact that exterior angles sum to 360 degrees, so one exterior angle of a regular polygon = 360 / number of sides; the interior angle is then 180 minus the exterior angle.
- Set up an equation using the relevant angle fact when a question gives an angle in terms of a letter, such as x or 2x, then solve for the unknown.
- State which angle rule you have used, and check that your answer is a sensible size for the type of angle described (acute, obtuse, reflex).
Worked example
In triangle ABC, angle A = 54 degrees and angle B = 71 degrees. Side BC is extended to a point D, so that angle ACD is the exterior angle of the triangle at C. (a) Calculate the size of angle ACB. (b) Hence calculate the size of the exterior angle ACD.
- Angles in a triangle add up to 180 degrees, so angle ACB = 180 - 54 - 71.
- 180 - 54 - 71 = 55 degrees. This is the answer to part (a).
- Angles on a straight line add up to 180 degrees, so angle ACD = 180 - angle ACB = 180 - 55.
- 180 - 55 = 125 degrees (this also equals 54 + 71, since the exterior angle equals the sum of the two opposite interior angles).
- (a) angle ACB = 55 degrees. (b) angle ACD = 125 degrees.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Two parallel lines are cut by a transversal. One of the angles formed is 68 degrees. State the size of the co-interior (allied) angle on the other parallel line, giving a reason.
The three angles of a triangle are 2x degrees, 3x degrees and 5x degrees. Calculate the value of x and hence find the size of each angle.
Two regular pentagons and one other shape are placed together so that they all meet at a single point with no overlap. Each regular pentagon has an interior angle of 108 degrees. Calculate the size of the third angle needed to exactly fill the point.
Free printable worksheet
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