Write down the answer to each question about angle facts.
(a)Write down the sum of the interior angles in any quadrilateral.(1)
(b)Write down the sum of the exterior angles of any polygon.(1)
(c)Write down the mathematical name given to two angles that add up to 90 degrees.(1)
(d)Write down the mathematical name given to two angles that add up to 180 degrees.(1)
(Total for Question 1 is 4 marks)
2
For each statement, write True or False. If the statement is False, write down the correct mathematical name for the angle described.
(a)An angle of 95 degrees is acute.(1)
(b)An angle of 180 degrees is called a straight-line angle.(1)
(c)An angle of 15 degrees is obtuse.(1)
(d)An angle of 300 degrees is reflex.(1)
(Total for Question 2 is 4 marks)
3
Two straight lines cross at a point, forming four angles. Circle the mathematical name for two of these angles that are on opposite sides of the crossing point and share no arm.
A) Corresponding B) Co-interior C) Vertically opposite D) Alternate
A) Corresponding
B) Co-interior
C) Vertically opposite
D) Alternate
(Total for Question 3 is 1 mark)
4
Circle the mathematical name for an angle of exactly 180 degrees.
A) Reflex angle B) Straight-line angle C) Obtuse angle D) Right angle
A) Reflex angle
B) Straight-line angle
C) Obtuse angle
D) Right angle
(Total for Question 4 is 1 mark)
5
Write down the number of right angles turned through in each case.
(a)Write down the number of right angles in a full turn.(1)
(b)Write down the number of right angles in three-quarters of a full turn.(1)
(Total for Question 5 is 2 marks)
6
The angle at vertex M in triangle LMN can be written as angle LMN. Write down one other three-letter name for this same angle.
(Total for Question 6 is 1 mark)
7
Two straight lines cross at a point. One of the four angles formed is 4x degrees. The angle vertically opposite to it measures 68 degrees.
Work out the value of x.
(Total for Question 7 is 2 marks)
8
At a roundabout, four roads meet, splitting the full turn around the roundabout into four angles. Three of the angles are equal, each measuring y, and the fourth measures 60 degrees.
Work out the size of angle y.
(Total for Question 8 is 2 marks)
9
Triangle XYZ has XY = XZ, so the triangle is isosceles. Angle Y = 72 degrees.
(a)Write down the size of angle Z. Give a reason for your answer.(2)
(b)Work out the size of angle X.(2)
(Total for Question 9 is 4 marks)
10
A triangular flag has angles of 55 degrees, 61 degrees and w.
(a)Work out the size of angle w.(2)
(b)Write down the mathematical name for a triangle in which all three angles, and all three sides, are different sizes.(1)
(Total for Question 10 is 3 marks)
11
A quadrilateral-shaped sign has angles in the ratio 2 : 3 : 4 : 6.
Work out the size of the smallest angle.
(Total for Question 11 is 3 marks)
12
Amelia is working out the size of angle x, where x and a 132 degree angle lie together on a straight line. She writes:
'x = 180 + 132 = 312 degrees'
(a)Identify the error in Amelia's method.(1)
(b)Work out the correct value of x.(1)
(Total for Question 12 is 2 marks)
13
ABCDEFGH is a regular octagon.
(a)Work out the size of each exterior angle of the octagon.(2)
(b)Work out the size of each interior angle of the octagon.(1)
(Total for Question 13 is 3 marks)
14
Angles e and f are supplementary. Angle e is three times the size of angle f.
Work out the size of angle f.
(Total for Question 14 is 2 marks)
15
A cyclist rides on a bearing of 048 degrees. She then turns and continues on a bearing of 132 degrees.
Work out the size of the angle through which she has turned.
(Total for Question 15 is 2 marks)
16
Two straight lines cross at point O, forming four angles. One of the angles is 63 degrees.
Work out the sizes of the other three angles.
(Total for Question 16 is 3 marks)
17
Two parallel lines are cut by a transversal. One of the angles formed measures 74 degrees. Angle m is alternate to this 74 degree angle.
Write down the size of angle m. Give a reason for your answer.
(Total for Question 17 is 2 marks)
18
Three angles, p, q and r, lie together on a straight line, where p = (x + 20) degrees, q = (2x + 10) degrees and r = (3x - 30) degrees.
(a)Show that x = 30.(3)
(b)Work out the size of the smallest of the three angles.(2)
(Total for Question 18 is 5 marks)
19
PQRS is a trapezium with PQ parallel to SR. Angle P = 108 degrees.
(a)Write down the size of angle S. Give a reason for your answer.(2)
(b)Angle Q = 95 degrees and angle R = w. Work out the size of angle w.(3)
(Total for Question 19 is 5 marks)
20
Each interior angle of a regular polygon is 156 degrees.
(a)Work out the size of one exterior angle of the polygon.(1)
(b)Work out the number of sides of the polygon.(2)
(c)Write down the mathematical name of a polygon with this number of sides.(1)
(Total for Question 20 is 4 marks)
Mark scheme · 2.10B Angles (Part 2)
Question 1
(a) B1 360 (degrees) cao
(a) Answer: 360 degrees
(b) B1 360 (degrees) cao
(b) Answer: 360 degrees
(c) B1 complementary cao
(c) Answer: Complementary
(d) B1 supplementary cao
(d) Answer: Supplementary
Question 2
(a) B1 False, obtuse oe
(a) Answer: False - it is obtuse (95 degrees is greater than 90 degrees).
(b) B1 True cao
(b) Answer: True
(c) B1 False, acute oe
(c) Answer: False - it is acute (15 degrees is less than 90 degrees).
(d) B1 True cao
(d) Answer: True
Question 3
B1 C circled, cao
Answer: C) Vertically opposite
Question 4
B1 B circled, cao
Answer: B) Straight-line angle
Question 5
(a) B1 4 cao
(a) Answer: 4
(b) B1 3 cao
(b) Answer: 3
Question 6
B1 NML oe
Answer: Angle NML
Question 7
M1 4x = 68 (vertically opposite angles are equal) oe
A1 x = 17 cao
Answer: x = 17
Question 8
M1 3y + 60 = 360 oe, or 3y = 300
A1 y = 100 cao
Answer: y = 100 degrees
Question 9
(a) B1 Z = 72 cao
(a) B1 correct reason given, e.g. base angles of an isosceles triangle are equal oe
(a) Answer: Z = 72 degrees
(b) M1 180 - 72 - 72
(b) A1 X = 36 cao
(b) Answer: X = 36 degrees
Question 10
(a) M1 180 - 55 - 61
(a) A1 w = 64 cao
(a) Answer: w = 64 degrees
(b) B1 scalene cao
(b) Answer: Scalene
Question 11
B1 states angles in a quadrilateral sum to 360 (degrees) oe
M1 360 / 15 (2 + 3 + 4 + 6 = 15 parts) oe
A1 48 cao
Answer: 48 degrees
Question 12
(a) B1 she should subtract 132 from 180, not add it, oe
(a) Answer: She added 132 to 180 instead of subtracting it from 180.
(b) B1 x = 48 cao
(b) Answer: x = 48 degrees
Question 13
(a) M1 360 / 8
(a) A1 45 cao
(a) Answer: 45 degrees
(b) B1 135, ft their exterior angle
(b) Answer: 135 degrees
Question 14
M1 e + f = 180 and e = 3f combined, e.g. 4f = 180 oe
A1 f = 45 cao
Answer: f = 45 degrees
Question 15
M1 132 - 48
A1 84 cao
Answer: 84 degrees
Question 16
B1 63 (degrees), the angle vertically opposite the given angle
B1 117 (degrees), one of the two angles adjacent to the given angle on a straight line
B1 117 (degrees) ft, the remaining angle, vertically opposite the other 117 degree angle
Answer: 63 degrees, 117 degrees and 117 degrees
Question 17
B1 m = 74 cao
B1 correct reason given, e.g. alternate angles are equal oe