State whether an angle of 152 degrees is acute, right angle, obtuse, straight or reflex.
(1)
2
A straight line is split into two angles by a ray. One angle is 47 degrees. Work out the size of the other angle.
(1)
3
Two straight lines cross. One of the angles formed is 76 degrees. Write down the size of the angle vertically opposite it.
(1)
4
In triangle XYZ, angle X = 52 degrees and angle Y = 61 degrees. Work out angle Z.
(1)
5
Write down the sum of the interior angles of any quadrilateral.
(1)
6
Two parallel lines are cut by a transversal. One angle is 84 degrees. Write down the size of its corresponding angle.
(1)
7
Write down the number of lines of symmetry of a regular pentagon.
(1)
8
A straight line is split into three angles: 35 degrees, 68 degrees and x. Work out x.
(2)
9
Four angles meet at a point. Three of the angles are 82 degrees, 77 degrees and 95 degrees. Work out the fourth angle, x.
(2)
10
Two straight lines PQ and RS cross at point O. Angle POR = 58 degrees. Work out the size of angle POS, giving a reason.
(2)
11
An isosceles triangle has an apex angle of 40 degrees. Work out the size of each base angle.
(2)
12
In a triangle, two of the interior angles are 48 degrees and 63 degrees. Work out the exterior angle at the third vertex.
(2)
13
Two parallel lines are cut by a transversal. One of the co-interior (allied) angles is 64 degrees. Work out the other co-interior angle.
(2)
14
A kite has one pair of equal angles of 108 degrees each. Work out the size of each of the other pair of equal angles.
(3)
15
Four angles of size 2x, 3x, 4x and x degrees meet at a point, with no other angles present. Find x, and hence work out the size of the largest angle.
(3)
16
Lines AB and CD are parallel, cut by a transversal EF. Angle P, where the transversal meets AB, is 115 degrees. Angle Q, at AB, is vertically opposite angle P. Angle R, at CD, is alternate to angle P. Angle S, at CD, is co-interior to angle P. Work out angles Q, R and S.
(3)
17
The three angles of a triangle are (2x + 15) degrees, (3x - 5) degrees and (x + 20) degrees. Find x, and hence work out the size of the largest angle in the triangle.
(3)
18
The interior angle of a regular polygon is 165 degrees.
(a)Work out the exterior angle of the polygon.(1)
(b)Hence work out the number of sides of the polygon.(2)
(c)Work out the sum of the interior angles of this polygon.(1)
19
A boat sails from harbour H to a buoy B on a bearing of 062 degrees. At B, the boat changes course and sails to a lighthouse L on a bearing of 155 degrees. Points H, B and L form a triangle.
(a)State the bearing of H from B.(1)
(b)Hence work out angle HBL, the interior angle of the triangle at B.(2)
(c)Given that angle BHL = 50 degrees, work out angle BLH.(2)
Mark scheme · KS3.M-G1D Geometry: Angles and Shapes: Fluency and Exam Drill
Question 1
B1 obtuse cao
Answer: obtuse
Question 2
B1 133 cao
Answer: 133 degrees
Question 3
B1 76 cao
Answer: 76 degrees
Question 4
B1 67 cao
Answer: 67 degrees
Question 5
B1 360 degrees cao
Answer: 360 degrees
Question 6
B1 84 cao
Answer: 84 degrees
Question 7
B1 5 cao
Answer: 5
Question 8
M1 set up 180 - 35 - 68 or equivalent method
A1 77 cao
Answer: 77 degrees
Question 9
M1 set up 360 - 82 - 77 - 95 or equivalent method
A1 106 cao
Answer: 106 degrees
Question 10
M1 recognise angles POR and POS lie on the straight line RS and sum to 180
A1 122 cao
Answer: 122 degrees
Question 11
M1 (180 - 40) / 2 or equivalent method
A1 70 cao
Answer: 70 degrees
Question 12
M1 use the exterior angle theorem, exterior angle = sum of the other two interior angles
A1 111 cao
Answer: 111 degrees
Question 13
M1 recognise co-interior angles sum to 180
A1 116 cao
Answer: 116 degrees
Question 14
M1 form 360 - 2(108) or equivalent method
M1 correctly evaluate 360 - 216 = 144
A1 72 cao
Answer: 72 degrees
Question 15
M1 form the equation 2x + 3x + 4x + x = 360, i.e. 10x = 360
M1 solve to get x = 36
A1 largest angle 144 degrees cao
Answer: x = 36; largest angle = 144 degrees
Question 16
B1 Q = 115 (vertically opposite angles are equal)
B1 R = 115 (alternate angles between parallel lines are equal)
B1 S = 65 (co-interior angles between parallel lines sum to 180)
Answer: Q = 115 degrees, R = 115 degrees, S = 65 degrees
Question 17
M1 form the equation (2x+15) + (3x-5) + (x+20) = 180, i.e. 6x + 30 = 180
M1 solve to get x = 25
A1 largest angle 70 degrees cao
Answer: x = 25; largest angle = 70 degrees
Question 18
(a) B1 15 cao
(a) Answer: 15 degrees
(b) M1 360 / 15 or equivalent method
(b) A1 24 cao
(b) Answer: 24
(c) B1 3960 cao
(c) Answer: 3960 degrees
Question 19
(a) B1 242 cao
(a) Answer: 242 degrees
(b) M1 find the difference between the bearing of H from B (242) and the bearing of L from B (155)