10 a Angles in a triangle add up to 180°. C1 2 C1 for clear explanation M You can split any quadrilateral into two C1 C1 for communication with clear diagram triangles. Therefore, the sum of the interior angles of any quadrilateral = 2 × 180o. For the two outside triangles, use the sum of the angles in triangle = 180° and the interior angle of a regular pentagon = 108°. 108° + 2x = 180° B1 B1 for showing inter angles of quadrilateral = 2 × 180 2x = 180° 108° – 2x = 72° b C1 C1 for a clear diagram correctly showing the three = 36° x triangles For the middle triangle, use interior angle of C1 C1 for identifying each angle of the triangles with regular pentagon = 108°. symbols showing which angles are equal = 108° y – x C1 C1 for clear explanation = 108° 36° y – M1 M1 for correct method of finding angle x = 72° y Using the sum of angles in triangle = 180°: = 180 2y z – = 180 144 z – A1 = 36o A1 for 36° z M1 M1 for correct method of finding angle Or 2x + = 108° y z = 36° x so 2 × 36° + = 108° z A1 + 72° = 108° A1 for 72° z = 36° z M1 M1 for correct method of finding angle z A1 A1 for 36° Two triangles with one angle = 108° C1 and two other equal angles of 36°. C1 for clear argument and stating assumptions used C1 One triangle with one angle = 36° and C1 for use of diagram with clarity of explanation two angles = 72°. 14
10 a b Angles in a triangle add up to 180°. You can split any quadrilateral into two triangles. Therefore, the sum of the interior angles of any quadrilateral = 2 × 180o. For the two outside triangles, use the sum of the angles in triangle = 180° and the interior angle of a regular pentagon = 108°. 108° + 2x = 180° 2x = 180° – 108° 2x = 72° x = 36° For the middle triangle, use interior angle of regular pentagon = 108°. y = 108° – x y = 108° – 36° y = 72° Using the sum of angles in triangle = 180°: z = 180 – 2y z = 180 – 144 z = 36o Or 2x + z = 108° x = 36° so 2 × 36° + z = 108° z + 72° = 108° z = 36° Two triangles with one angle = 108° and two other equal angles of 36°. One triangle with one angle = 36° and two angles = 72°. C1 C1 B1 C1 C1 C1 M1 A1 M1 A1 M1 A1 C1 C1 2 C1 for clear explanation C1 for communication with clear diagram B1 for showing inter angles of quadrilateral = 2 × 180 C1 for a clear diagram correctly showing the three triangles C1 for identifying each angle of the triangles with symbols showing which angles are equal C1 for clear explanation M1 for correct method of finding angle x A1 for 36° M1 for correct method of finding angle y A1 for 72° M1 for correct method of finding angle z A1 for 36° C1 for clear argument and stating assumptions used C1 for use of diagram with clarity of explanation M 14
Higher_Skills_Geometry_MarkScheme_Edexcel.docx