Last reviewed: 10 November 2026
Updated November 2026. These Grade 7 angles notes cover angles on a straight line and at a point, angles on a transversal, angles in a parallelogram, and the angle properties of polygons up to hexagons. The key facts: angles on a straight line add up to 180°, angles at a point add up to 360°, the interior angles of a polygon with n sides add up to (n − 2) × 180°, and the exterior angles of any convex polygon add up to 360°.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 7 maths topics, see our Grade 7 mathematics revision guide and the Grade 7 notes hub.
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What the Grade 7 Curriculum Covers
Angles is a sub-strand under Geometry in the Kenya Institute of Curriculum Development’s Grade 7 Mathematics design. Learners relate angles on a straight line, solve angles at a point, relate angles on a transversal, solve angles in a parallelogram, and relate interior angles, exterior angles and the number of sides of polygons up to hexagons. The design is listed on the KICD Grade Seven curriculum designs page.
Angles on a Straight Line and at a Point
Angle facts and names used here follow OpenStax Contemporary Mathematics’ section on angles.
- Angles on a straight line add up to 180°. If one is 115°, the other is 65°.
- Angles at a point add up to 360°. If three angles at a point are 90°, 130° and x, then x = 360 − 220 = 140°.
- Vertically opposite angles (formed where two lines cross) are equal.
Worked example
Angles on a straight line are 2x and 3x + 30°. Then 2x + 3x + 30 = 180, so 5x = 150 and x = 30°. The angles are 60° and 120°.
Angles on a Transversal
A transversal is a line crossing two or more other lines. When it crosses two parallel lines:
- Corresponding angles are equal (the “F” shape).
- Alternate angles are equal (the “Z” shape).
- Co-interior angles add up to 180° (the “C” or “U” shape).
Example: a transversal makes an angle of 72° with one parallel line. The alternate angle is 72° and the co-interior angle is 180 − 72 = 108°. These rules work only when the lines are parallel.
Angles in a Parallelogram
A parallelogram has two pairs of parallel sides. So opposite angles are equal and adjacent angles add up to 180° (they are co-interior angles). If one angle is 65°, the angles are 65°, 115°, 65° and 115°. Check: they add up to 360°.
Angle Properties of Polygons up to Hexagons
A polygon with n sides can be split into (n − 2) triangles from one vertex, so its interior angles add up to (n − 2) × 180°. At each vertex, the interior and exterior angles lie on a straight line, so they add up to 180°. Walking round a convex polygon you turn through one full turn, so the exterior angles add up to 360°. These properties are discussed in OpenStax Contemporary Mathematics’ section on polygons.
| Polygon | Sides | Sum of interior angles | Each interior angle (regular) | Each exterior angle (regular) |
|---|---|---|---|---|
| Triangle | 3 | 180° | 60° | 120° |
| Quadrilateral | 4 | 360° | 90° | 90° |
| Pentagon | 5 | 540° | 108° | 72° |
| Hexagon | 6 | 720° | 120° | 60° |
Worked example: finding the number of sides
Each exterior angle of a regular polygon is 72°. Number of sides = 360 ÷ 72 = 5, so it is a pentagon.
Worked example: a missing angle
A pentagon has angles 100°, 110°, 95°, 120° and x. Sum = 540°, so x = 540 − 425 = 115°.
Original Practice Questions With Worked Answers
- Two angles on a straight line are x and 2x. Find x. 3x = 180, x = 60°.
- Angles at a point are 85°, 120°, 95° and y. Find y. y = 360 − 300 = 60°.
- A transversal crosses two parallel lines, making a 48° angle. Find its co-interior angle. 132°.
- One angle of a parallelogram is 108°. Find the other three. 72°, 108°, 72°.
- Find each interior angle of a regular hexagon. 720 ÷ 6 = 120°.
Cover the answers and attempt each question first. For timed practice, use the Grade 7 revision papers or the Grade 7 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What do angles on a straight line add up to?
180°.
How do you find the sum of interior angles of a polygon?
Use (n − 2) × 180°, where n is the number of sides. A hexagon has (6 − 2) × 180° = 720°.
What is the difference between alternate and corresponding angles?
Both are equal when lines are parallel. Alternate angles are on opposite sides of the transversal (Z shape); corresponding angles are in matching positions (F shape).
What do the exterior angles of a polygon add up to?
360°, for any convex polygon.