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Geometry
Geometry

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Question 1

  • (a) How would you refer to angle α in this triangle by means of the letters A, B and C?

  • (b) Measure α with a protractor , if you have one, or otherwise estimate it.

  • (c) What type of angle is α?

  • (d) Find β without using a protractor using the fact that the three angles of a triangle always add up to 180°.

Answer

  • (a) Any of the following could be used: , , BAC, , CAB.

  • (b) α = 80°.

  • (c) Because α is less than 90°, it is an acute angle.

  • (d) As the three angles of a triangle always add up to 180°,

  • Therefore

Question 2

2 This pie chart shows the proportions of people voting for four parties in a local election.

  • (a) Measure the angles of the four slices of the pie with your protractor or estimate them if you don't have a protractor.

  • (b) Check your measurements by ensuring that the angles add up to 360°.

  • (c) Work out the percentage of the total vote polled by each of the four parties.

Answer

  • (a) Red party: 120°.

    Blue party: 95°.

    Yellow party: 95°.

    Green party: 50°.

  • (b) 120° + 95° + 95° + 50° = 360°.

  • (c) Since 360° represents 100%, 1° will represent or .

  • So the Red party polled

    The Blue party and the Yellow party polled

    The Green party polled