About this video
How to find unknown angles in a triangle using the fact that the three interior angles always add up to 180°.
What it covers
- The angles of a triangle add up to 180°
- A bisector splits an angle into two equal parts
- Isosceles: equal sides, equal opposite angles; equilateral: 60° each
- Reasons: '∠s of a △', 'isos △', 'given', '∠s on a str line'
- Setting up an equation to solve for x
Extra worked examples
✍️ Extra example: in △ABC, Â = 52° and B̂ = 90° (given). BD bisects B̂ and meets AC at D. Find Ĉ and AB̂D.
- 1Ĉ = 180° − 52° − 90° = 38°∠s of a △ add up to 180°.
- 2AB̂D = 90° ÷ 2 = 45°BD bisects the right angle: two equal parts.
- 3In △ABD: AD̂B = 180° − 52° − 45° = 83°Always find every angle you can — then write each with its reason.
✍️ Extra example: in △PQR, PQ = PR, Q̂ = 2x + 10° and R̂ = 3x − 15°. Find x and P̂.
- 12x + 10° = 3x − 15°Isos △: the angles opposite the equal sides are equal.
- 2x = 25° → Q̂ = R̂ = 60°Solve, then substitute in brackets.
- 3P̂ = 180° − 60° − 60° = 60°All three angles are 60° — the triangle is equilateral.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Two angles of a triangle are 47° and 68°. Find the third angle.
Show answer ▾Hide answer ▴
180° − 47° − 68° = 65° (∠s of a △) - 2An isosceles triangle has a 40° angle between its equal sides. Find each base angle.
Show answer ▾Hide answer ▴
(180° − 40°) ÷ 2 = 70° each (isos △) - 3The angles of a triangle are x, 2x and 3x. Find x.
Show answer ▾Hide answer ▴
6x = 180° → x = 30° - 4In △KLM, K̂ = 90° (given) and KN bisects K̂. Find each part of K̂.
Show answer ▾Hide answer ▴
90° ÷ 2 = 45° each (KN bisects the angle) - 5All three sides of a triangle are equal. Find each angle and give the reason.
Show answer ▾Hide answer ▴
x + x + x = 180° (∠s of a △) → x = 60° each (equilateral △)
Read the full lesson
Practise this topic
Download matching Grade 8–9 papers and worksheets.
