Angles · Usually met around P6
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 add up to 180°. A quadrilateral's four angles add up to 360°, because a diagonal cuts it into two triangles: 180 × 2 = 360. So x is the total minus the angles you know. Quicker: add the known angles first, then take them away in one go. A quadrilateral with 80°, 95° and 110°: 80 + 95 = 175, 175 + 110 = 285, 360 − 285 = 75, x = 75°. A right-angle mark means 90°, so count it too. An isosceles triangle (two sides with the same mark) has equal base angles. With a top angle of 40°: 180 − 40 = 140, 140 ÷ 2 = 70, so each base angle is 70°. Another way is to take the known angles from the total one by one: 360 − 80 − 95 − 110 = 75.
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 = 70°
An isosceles triangle's two base angles are equal, both 55°: 55 + 55 = 110, 180 − 110 = 70, so x = 70°
Example 2
Triangle: ∠x = ?°
Show the answer and working
Answer: Triangle: ∠x = 85°
A triangle's three angles make 180°: add the angles you know first, 60 + 35 = 95, 180 − 95 = 85, so x = 85°
Example 3
Triangle: ∠x = ?°
Show the answer and working
Answer: Triangle: ∠x = 25°
A triangle's three angles make 180°: add the angles you know first, 100 + 55 = 155, 180 − 155 = 25, so x = 25°
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