Interior Angles Of A Polygon Gcse Maths Steps Examples We will call these angles x: we know that angles around a point add to 360°. therefore: 60 2x =360 2x =300 x =150 60 2 x = 360 2 x = 300 x = 150. this means that each interior angle of the regular polygon is 150°. so the sum of interior angles is equal to 150 × n or 150n: 150n = (n – 2) × 180. we can now solve for n:. The polygon can be broken up into three triangles. multiply the number of triangles by 180o to get the sum of the interior angles. show step. 180∘ ×3 = 540∘ 180 ∘ × 3 = 540 ∘. state your findings e.g. sides, regular irregular, the sum of interior angles. show step.
Interior Angles Of A Polygon Gcse Maths Steps Examples \text{sum of interior angles}=180(n 2). one interior angle of a regular polygon with n sides is determined using the formula, \theta=\frac{180(n 2)}{n}. for an irregular polygon, the missing angle is calculated by subtracting all of the known angles from the total sum of the interior angles of the polygon. exterior angles; the sum of exterior. If it is a regular polygon (all sides are equal, all angles are equal) shape sides sum of interior angles shape each angle; triangle: 3: 180° 60° quadrilateral: 4: 360° 90° pentagon: 5: 540° 108° hexagon: 6: 720° 120° heptagon (or septagon) 7: 900° 128.57 ° octagon: 8: 1080° 135° nonagon: 9: 1260° 140° any polygon: n (n−2. Interior and exterior angles example questions. question 1: the shape below is a regular pentagon. work out the size of the interior angle, x. [2 marks] level 4 5 gcse ks3 aqa edexcel ocr wjec edexcel igcse. show answer. question 2: the shape below is a regular octagon. work out the size of the interior angle, x. Regular polygons have equal length sides, interior angles, and exterior angles. we can calculate interior and exterior angles when we know the number of sides the regular polygon has: exterior angles: \dfrac{360\degree}{\textcolor{green}{n}} where \textcolor{green}{n} is the number of sides. interior angles: 180\degree exterior angle size.
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