Unit 3 Angles on Parallel Line and Polygons
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Unit 3 Angles on Parallel Line and Polygons
1. In the diagram, AB is parallel to CD.
A C Not drawn accurately 112° x
130° y
B D
(a) State the value of x. Give a reason for your answer. (2)
(b) Find the value of y. (2) (Total 4 marks)
2.
b
a
Not drawn accurately
c
70º 60º
Work out the values of a, b and c. (Total 3 marks)
Hinchingbrooke School 1 Unit 3 Angles on Parallel Line and Polygons
3. (a) Work out the size of angles a and b.
a
20°
b Not drawn accurately
40°
(3)
(b) Show that x + y + z = 180
A
B x y C Not drawn accurately D z E
(2) (Total 5 marks)
4. (a) The diagram shows a quadrilateral.
97°
131° Not drawn accurately 72°
x
Work out the value of x. (3)
Hinchingbrooke School 2 Unit 3 Angles on Parallel Line and Polygons
(b) The diagram shows an isosceles triangle.
30° Not drawn accurately
p q
(i) Work out the value of p. (2)
(ii) Work out the value of q. (1)
5. Calculate the size of an interior angle of a regular octagon. (Total 3 marks)
6. (a) Triangle PQR is isosceles. PQ = PR Angle R = 44°
P
Not drawn accurately
44° Q R
Calculate the size of angle P. (2)
(b) The words in this list are used to describe angles.
alternate corresponding exterior interior opposite
Hinchingbrooke School 3 Unit 3 Angles on Parallel Line and Polygons
c e
Not drawn accurately
d
Choose a word from the list to describe each of these pairs of angles.
(i) c and d are ...... angles (1)
(ii) d and e are ...... angles (1)
7. A triangle has angles of 63°, 2x and x.
2x Not drawn accurately
x 63°
Work out the value of x. (Total 3 marks)
8. The diagram shows part of a regular polygon. Each interior angle is 144°.
Not drawn accurately
144°
Calculate the size of the exterior angle of the polygon. (Total 2 marks)
9. (a) ABCDE is a regular pentagon.
Hinchingbrooke School 4 Unit 3 Angles on Parallel Line and Polygons
C Not drawn accurately
B x D
A E
Work out the value of the interior angle x. (2)
(b) ABCDE is a regular pentagon.
C Not drawn accurately
B D
y A E
Work out the value of y. (2) (Total 4 marks)
10. The diagram shows part of a regular polygon.
Each interior angle is 162°.
Not drawn accurately
162°
Calculate the number of sides of the polygon. (Total 3 marks)
11. ABC is an isosceles triangle. BCDE is a kite.
Hinchingbrooke School 5 Unit 3 Angles on Parallel Line and Polygons
A
40°
D x Not drawn accurately C E
40°
B
Work out the value of x. (Total 3 marks)
12. The diagram shows a regular decagon.
Not drawn accurately
y
x
(a) Work out the angle at the centre of the decagon, marked x on the diagram. (2)
(b) Work out the size of the interior angle, marked y on the diagram. (2) (Total 4 marks)
13. The angles of a quadrilateral are 73°, 2x°, 3x° and 102°.
Hinchingbrooke School 6 Unit 3 Angles on Parallel Line and Polygons
73° Not drawn accurately 102°
3x ° 2x °
(a) Write down an equation in x. (2)
(b) Use your equation to find the largest angle in the quadrilateral. (3)
14. ABCD is a rhombus and ABCE is a kite.
B 110º
A C x
D Not drawn accurately
50º
E
Work out the value of x. (Total 4 marks)
15. (a) A regular polygon has 9 sides. Calculate the size of an interior angle. (2)
(b) Explain why there is no regular polygon which has an interior angle of 155. (3) (Total 5 marks)
16. The lines AB and CD are parallel.
Hinchingbrooke School 7 Unit 3 Angles on Parallel Line and Polygons
B Not drawn accurately
p D r 40°
A
q
50° C
(a) Write down the value of p Give a reason for your answer. (2)
(b) Write down the value of q. Give a reason for your answer.
(2)
(c) Work out the value of r. (2) (Total 6 marks)
Hinchingbrooke School 8