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