ZIMSEC O Level · Mathematics · Form 1, Form 2, Form 3, Form 4
Angle facts
- Angles on a straight line add to 180°; angles at a point add to 360°.
- Vertically opposite angles are equal.
- Parallel lines: alternate angles are equal, corresponding angles are equal, co-interior angles add to 180°.
- Angles in a triangle add to 180°; in a quadrilateral, 360°.
Polygons
- Sum of interior angles of an n-sided polygon = (n − 2) × 180°.
- Exterior angles of any polygon add to 360°. In a regular polygon each exterior angle = 360° ÷ n.
Worked example: Each interior angle of a regular polygon is 144°. How many sides does it have?
Exterior angle = 180° − 144° = 36°. n = 360 ÷ 36 = 10 sides.
Similarity and congruency (Form 3–4)
- Similar shapes have equal angles and sides in the same ratio k. Areas scale by k² and volumes by k³.
- Congruent triangles are identical: test with SSS, SAS, ASA or RHS.
Circle theorems (Form 4)
- The angle at the centre is twice the angle at the circumference.
- Angles in the same segment are equal; the angle in a semicircle is 90°.
- Opposite angles of a cyclic quadrilateral add to 180°.
- A tangent is perpendicular to the radius at the point of contact.
Constructions
Use a ruler and compasses only: bisect lines and angles, and construct 60°, 90°, 45° and 30° angles. Leave construction arcs visible.
Exam tip: Give a reason for every angle you find, e.g. “alternate angles” – reasons carry marks.
Check yourself
- Find the sum of the interior angles of a hexagon.
- Two similar triangles have corresponding sides 4 cm and 6 cm. The smaller has area 20 cm². Find the area of the larger.
- In a cyclic quadrilateral ABCD, angle A = 75°. Find angle C.
Show answers
- 720°
- k = 1.5, area = 20 × 2.25 = 45 cm²
- 105°
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