Stage 11 · Shape & space
Angles in triangles and quadrilaterals
Triangle 180°, quadrilateral 360°.
How to do it
Method
Triangle 180°, quadrilateral 360°
80 + 95 + 110 = 285, 360 − 285 = 75
Another way
Take each away
360 − 80 − 95 − 110 = 75
In full
A triangle's three angles make 180°; a quadrilateral's four make 360°, since a diagonal cuts it into two triangles: 180 × 2 = 360. So x is the total less the angles you know. Quicker: add the known angles first, then take away once: a quadrilateral with 80°, 95° and 110°, 80 + 95 = 175, 175 + 110 = 285, 360 − 285 = 75, x = 75°. A right-angle mark means 90°: count it too. An isosceles triangle (two sides with the same mark) has equal base angles: a top angle of 40°, 180 − 40 = 140, 140 ÷ 2 = 70, so each base angle is 70°. Another way: take the known angles from the total one by one: 360 − 80 − 95 − 110 = 75 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Isosceles triangle: ∠x = ?°
Show the answer and working
Answer: Isosceles triangle: ∠x = 40°
An isosceles triangle's two base angles are equal, both 70°: 70 + 70 = 140, 180 − 140 = 40, so x = 40°
Example 2
Triangle: ∠x = ?°
Show the answer and working
Answer: Triangle: ∠x = 92°
A triangle's three angles make 180°: add the angles you know first, 28 + 60 = 88, 180 − 88 = 92, so x = 92°
Example 3
Right-angled trapezium: ∠x = ?°
Show the answer and working
Answer: Right-angled trapezium: ∠x = 108°
A quadrilateral's four angles make 360°, two of them right angles: 90 + 90 = 180, 180 + 72 = 252, 360 − 252 = 108, so x = 108°
Example 4
Quadrilateral: ∠x = ?°
Show the answer and working
Answer: Quadrilateral: ∠x = 95°
A quadrilateral's four angles make 360°: add the angles you know first, 135 + 61 = 196, 196 + 69 = 265, 360 − 265 = 95, so x = 95°
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