The pattern
Angle and shape properties
Mark the shape property first, then subtract known angles from the relevant total.
A rhombus or parallelogram carries the same fact wherever it appears: opposite angles match, and a straight line always makes 180°. Once your child spots that two lines crossing at a point make four angles, with the ones facing each other equal, the diagram starts filling itself in. Each new angle you find hands you the next one, until the one being asked for is the only one left.
How to spot it
Look for a named quadrilateral like a rhombus or parallelogram, plus two straight lines crossing inside or through it. Words like "straight line" and "collinear" point to this move.
Common mistake
Children mix up which angle sits opposite which once lines cross at a point away from the main shape. Trace each ray back to its two labelled ends before deciding what faces what.
31 worked solutions
Standard
- angles around a point Three angles around a point are 85°, 65° and 120°. Find the remaining angle.
- angles around a point Three angles around a point are 70°, 110° and 90°. Find the remaining angle.
- angles on a straight line One angle on a straight line is 47°. Find the adjacent angle.
- angles on a straight line One angle on a straight line is 125°. Find the adjacent angle.
- compare with a right angle Is the shown 45° angle smaller or larger than a right angle?
- compare with a right angle Is the shown 120° angle smaller or larger than a right angle?
- draw an angle Draw an angle of 35°.
- draw an angle Draw an angle of 110°.
- equilateral triangle angles Find each interior angle of an equilateral triangle.
- isosceles triangle angles An isosceles triangle has a vertex angle of 80°. Find each equal base angle.
- isosceles triangle angles An isosceles triangle has a vertex angle of 52°. Find each equal base angle.
- measure an angle Measure the smaller angle shown in the figure.
- measure an angle Measure the smaller angle shown in the figure.
- name an angle The shown angle is formed by rays OA and OB. Name the angle at O using three-letter notation.
- name an angle The shown angle is formed by rays OA and OB. Name the angle at O using three-letter notation.
- parallelogram angles One angle of a parallelogram is 74°. Find an adjacent angle.
- parallelogram angles One angle of a parallelogram is 105°. Find an adjacent angle.
- recognise an angle What geometric idea is marked at the larger turn where the two shown rays share an endpoint?
- recognise an angle What geometric idea is marked at the smaller turn where the two shown rays share an endpoint?
- rhombus angles One angle of a rhombus is 84°. Find the opposite angle.
- rhombus angles One angle of a rhombus is 110°. Find the opposite angle.
- right triangle angles A right triangle has another angle of 62°. Find its third angle.
- right triangle angles A right triangle has another angle of 48°. Find its third angle.
- trapezium angles Two angles on the same non-parallel side of a trapezium lie between its parallel bases. One is 76°. Find the other.
- trapezium angles Two angles on the same non-parallel side of a trapezium lie between its parallel bases. One is 108°. Find the other.
- triangle angle total Two angles of a triangle are 73° and 44°. Find the third angle.
- triangle angle total Two angles of a triangle are 38° and 92°. Find the third angle.
- unknown angle in a quadrilateral Three interior angles of a quadrilateral are 85°, 95° and 120°. Find the fourth angle.
- unknown angle in a quadrilateral Three interior angles of a quadrilateral are 70°, 115° and 80°. Find the fourth angle.
- vertically opposite angles Two straight lines cross. One angle is 72°. Find its vertically opposite angle.
- vertically opposite angles Two straight lines cross. One angle is 118°. Find its vertically opposite angle.
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.