Learning pack · IGCSE handout

Angles

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Angle facts underpin almost every shape question: vertically opposite angles, angles on a straight line, and angles around a point. The handout drills recognition and multi-step reasoning; the answers PDF shows the marking-style layout.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 1_angles_handout.pdf · 1_angles_handout_answers.pdf

Full topic summary

Angle facts underpin almost every shape question: vertically opposite angles, angles on a straight line, and angles around a point. The handout drills recognition and multi-step reasoning; the answers PDF shows the marking-style layout.

Key learning points

Angles on a straight line sum to $180^\circ$ ; around a point to $360^\circ$ .
Vertically opposite angles are equal.
In a triangle, interior angles sum to $180^\circ$ ; exterior angle equals the sum of the two remote interiors.
Parallel lines: corresponding equal, alternate equal, co-interior sum to $180^\circ$ .

Worked example 1 — Straight line

Angles on a straight line: $x$ and $65^\circ$ . Find $x$ .

Working

x=180-65=115

Sum to $180^\circ$ .

Worked example 2 — Around a point

Angles $x$ , $90^\circ$ , $120^\circ$ around a point. Find $x$ .

Working

x=360-90-120=150

Sum to $360^\circ$ .

Worked example 3 — Triangle sum

Triangle angles $50^\circ$ , $60^\circ$ , $x$ . Find $x$ .

Working

x=70

Sum to $180^\circ$ .

Worked example 4 — Parallel lines

Alternate angle to $72^\circ$ is $x$ . Find $x$ .

Working

x=72

Alternate angles are equal.

Worked example 5 — Exterior angle

Exterior angle of a triangle is $110^\circ$ . One remote interior is $40^\circ$ . Find the other.

Working

x=110-40=70

Exterior = sum of the two remote interiors.

🎬 Topic videos

Pascal's Triangle - Numberphile
Numberphile · 13 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
All Triangles are Equilateral - Numberphile
Numberphile · 5 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Triangles have a Magic Highway - Numberphile
Numberphile · 10 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Too Many Triangles - Numberphile
Numberphile · 8 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Squaring the Triangle - Numberphile
Numberphile · 14 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
3 Ways to Draw Squares Inside Triangles - Numberphile
Numberphile · 9 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.

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Browse the hub Learning Packs & Summary, or open the compact Angles summary.