Geometry: Angles and Shapes
Angles and shapes covers the angle facts and polygon properties used throughout KS3 geometry: angles on a straight line, angles around a point, angles in triangles and quadrilaterals, and angles formed with parallel lines. It also includes naming polygons, describing symmetry, and working with bearings. These facts are essential building blocks for GCSE geometry questions that combine several angle rules.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Identify which angle fact applies: angles on a straight line sum to 180 degrees, angles round a point sum to 360 degrees, angles in a triangle sum to 180 degrees, and angles in a quadrilateral sum to 360 degrees.
- For parallel lines cut by a transversal, spot corresponding angles (equal, same position), alternate angles (equal, Z-shape) and co-interior angles (sum to 180 degrees, C-shape).
- Set up an equation using the relevant angle fact, using a letter for the unknown angle.
- Solve the equation to find the unknown angle, showing each step of your working.
- For polygons, use (n - 2) x 180 degrees for the interior angle sum, and 360 degrees divided by the number of sides for the exterior angle of a regular polygon.
- Always state the correct geometric reason alongside your numerical answer.
Worked example
Lines AB and CD are parallel, cut by a transversal EF. One angle formed at the intersection with line AB is 74 degrees. Find the size of the co-interior angle at the intersection with line CD, giving a reason.
- Co-interior (allied) angles between parallel lines always sum to 180 degrees.
- Set up the equation: co-interior angle + 74 = 180.
- Solve: co-interior angle = 180 - 74 = 106.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
An isosceles triangle has two equal base angles of x degrees. The apex angle is (x + 45) degrees. Form an equation in x, and solve it to find the size of the apex angle.
The interior angle sum of a polygon with n sides is (n - 2) x 180 degrees. Work out the sum of the interior angles of an octagon (8 sides).
A hexagon has interior angles 128, 115, 140, 108, 135 and x degrees. Work out x. Then a regular polygon has an exterior angle of 18 degrees; work out the number of sides of this polygon.
Free printable worksheet
Want more practice on paper? Download the geometry: angles and shapes worksheet pack - 15 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
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