Write down the sum of the interior angles of a hexagon.
(1)
2
Find the exterior angle of a regular nonagon (9 sides).
(1)
3
A regular decagon (10 sides) has all interior angles equal. Calculate the size of one interior angle.
(1)
4
Write down the sum of the interior angles of a triangle.
(1)
5
Calculate the exterior angle of a regular dodecagon (12 sides).
(1)
6
An irregular quadrilateral has interior angles 80 degrees, 95 degrees and 110 degrees. Work out the missing interior angle.
(1)
7
Each exterior angle of a regular polygon is 20 degrees. How many sides does the polygon have?
(1)
8
A regular polygon has each interior angle equal to 140 degrees. Find the number of sides of the polygon.
(2)
9
An irregular pentagon has interior angles 100 degrees, 95 degrees, 88 degrees and 102 degrees. Work out the missing interior angle.
(2)
10
A regular polygon has 20 sides. Calculate the size of one interior angle.
(2)
11
Each exterior angle of a regular polygon is 15 degrees. How many sides does the polygon have?
(2)
12
The interior angles of a quadrilateral add to 360 degrees. Two of the angles are equal (each y) and the other two are 100 degrees and 90 degrees. Find the size of y.
(2)
13
A regular polygon has interior angle 156 degrees. Work out n, the number of sides.
(2)
14
The angles in a pentagon are in the ratio 4:5:6:7:8. Find the size, in degrees, of the largest angle.
(3)
15
A regular polygon has n sides. The sum of its interior angles is 3060 degrees. Work out n.
(3)
16
In a regular polygon, four exterior angles are removed and their total is 100 degrees. The remaining exterior angles are all equal and there are 14 exterior angles in total. Work out the size of one of the remaining exterior angles.
(3)
17
The interior angles of a convex hexagon are in arithmetic progression. The smallest angle is 80 degrees and the largest is 160 degrees. Work out the common difference between consecutive angles.
(3)
18
A regular polygon is joined to its centre to form isosceles triangles. Each triangle has a vertex angle of 18 degrees at the centre.
(a)Work out how many sides the polygon has.(1)
(b)Each isosceles triangle has two equal base angles. Work out the size of one base angle.(2)
(c)Hence state the size of one interior angle of the polygon.(1)
19
A polygon has 9 sides. Eight of its interior angles are equal, each measuring 142 degrees. The ninth angle is r degrees.
(a)Work out the sum of the interior angles of a 9-sided polygon.(1)
(b)Hence work out r.(2)
(c)A different, regular nonagon has all 9 angles equal. Work out the size of one interior angle of this regular nonagon, and state whether it is bigger or smaller than r found in part (b).(2)
Mark scheme · KS3.M-G10D Angles in Polygons: Fluency and Exam Drill
Question 1
B1 720 cao
Answer: 720 degrees
Question 2
B1 40 cao
Answer: 40 degrees
Question 3
B1 144 cao
Answer: 144 degrees
Question 4
B1 180 cao
Answer: 180 degrees
Question 5
B1 30 cao
Answer: 30 degrees
Question 6
B1 75 cao
Answer: 75 degrees
Question 7
B1 18 cao
Answer: 18
Question 8
M1 find exterior angle 180 - 140 = 40
A1 9 cao
Answer: 9
Question 9
M1 use pentagon angle sum 540 and subtract the four known angles
A1 155 cao
Answer: 155 degrees
Question 10
M1 find the sum of interior angles (20-2) x 180 = 3240
A1 162 cao
Answer: 162 degrees
Question 11
M1 360 / 15 or equivalent method
A1 24 cao
Answer: 24
Question 12
M1 form the equation 2y + 100 + 90 = 360
A1 85 cao
Answer: 85 degrees
Question 13
M1 find exterior angle 180 - 156 = 24
A1 15 cao
Answer: 15
Question 14
M1 use the pentagon angle sum of 540 degrees
M1 divide 540 by the total number of parts, 4+5+6+7+8=30, to get 18 per part
A1 144 cao
Answer: 144 degrees
Question 15
M1 use (n-2) x 180 = 3060
M1 solve n - 2 = 3060 / 180 = 17
A1 19 cao
Answer: 19
Question 16
M1 subtract the removed total from 360: 360 - 100 = 260
M1 find the number of remaining angles: 14 - 4 = 10
A1 26 cao
Answer: 26 degrees
Question 17
M1 hexagon angle sum is 720, giving an average angle of 720/6 = 120, matching (80+160)/2
M1 there are 5 equal gaps between the smallest and largest of the 6 terms
A1 16 cao
Answer: 16 degrees
Question 18
(a) B1 20 cao
(a) Answer: 20
(b) M1 180 - 18 = 162, then divide by 2
(b) A1 81 cao
(b) Answer: 81 degrees
(c) B1 162 cao
(c) Answer: 162 degrees
Question 19
(a) B1 1260 cao
(a) Answer: 1260 degrees
(b) M1 8 x 142 = 1136, then 1260 - 1136
(b) A1 124 cao
(b) Answer: 124 degrees
(c) M1 1260 / 9 = 140
(c) A1 140 degrees, which is bigger than r = 124, cao
(c) Answer: 140 degrees; bigger than r (124 degrees)