Vertically opposite angles
Two or three straight lines cross at one point, and the sizes of some of the angles between them are given. The student types the size of the angle marked x, in degrees. The lines are drawn to size and turned a different way each time: as plain lines, as lines a child draws, as roads at a junction, as paths in a park, or as straight cuts across a round cake through its centre.
Two facts do all the work: vertically opposite angles are equal, and angles side by side on a straight line add to 180°. The classic slip is using the wrong one: taking the given angle from 180° when x sits across the crossing from it, or copying it when x is not opposite it. With three lines, x is often next to neither given angle, so the student first copies one of them to its opposite angle, which sits next to x, and then uses the straight line. Some questions give one angle as a right angle, marked only by its small square. The working shades the angles each step uses and draws the straight line it uses in red.
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What changes each time
- Two lines with one angle given, x beside it or opposite it; or three lines through one point with two angles given, where x may need an angle copied across first
- Whole-degree angles: 20° to 160° with two lines and 25° to 130° with three, and about a quarter of the three-line questions give a right angle by its square
- Plain lines, a child's drawing, roads at a junction, park paths or a cake cut through its centre, turned a different way each time
More shapes and angles practice
- Sides and corners of 2D shapes (Grade 2)
- Faces, edges and vertices (Grade 3)
- Sorting quadrilaterals (Grade 3)
- Turning and flipping letters (Grade 3)
- Counting squares of every size (Grade 3)
- Inside or outside the loop (Grade 3)
- Which piece fills the gap? (Grade 3)
- Symmetry on a grid (Grade 4)
- Rotations and reflections (Grade 4)
- Reading a protractor (Grade 4)
- Parallel and perpendicular lines (Grade 4)
- Parts of a circle (Grade 4)
- Draw without lifting your pencil (Grade 4)
- Can these sticks make a triangle? (Grade 4)
- Lines, rays and line segments (Grade 4)
- Counting line segments (Grade 4)
- Triangle from two circles (Grade 4)
- Splitting an angle in half (Grade 4)
- 3D shapes: side view (Grade 5)
- Rectangle in a quarter circle (Grade 5)
- Painted cube puzzle (Grade 5)
- Rope around the Earth (Grade 5)
- Can dominoes cover the board? (Grade 5)
- Most crossing points of straight lines (Grade 5)
- Equal radii: find the missing length (Grade 5)
- Angles in a circle (Grade 6)
- Congruent triangles: match the corners first (Grade 6)
- Inscribed circle in a right triangle (Grade 8)
- SSS and SAS: is it enough to prove congruence? (Grade 8)