Angles summary

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

Sum to $180^\circ$.

Worked example 2 — Around a point

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

Working

Sum to $360^\circ$.

Worked example 3 — Triangle sum

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

Working

Sum to $180^\circ$.

Worked example 4 — Parallel lines

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

Working

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

Exterior = sum of the two remote interiors.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.