WEBVTT
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The diagram below shows the positions of four points π΄, π΅, πΆ, and π· on a map.
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π΄π΅ is parallel to πΆπ·.
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π·π΄ is parallel to π΅πΆ.
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The bearing of π΅ from π΄ is 082 degrees.
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Angle π΄π΅πΆ is 43 degrees.
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Work out the bearing of π· from π΄.
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All bearings are measured clockwise from north.
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This means that the bearing of π΅ from π΄ of 082 degrees can be drawn on the diagram as shown.
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As the quadrilateral is made up of two pairs of parallel sides and the angles are not 90 degrees, we can say that π΄π΅πΆπ· is a parallelogram.
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Adjacent angles in a parallelogram add up to 180 degrees.
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Therefore, angle π΄π΅πΆ and angle π΅π΄π· equal 180 degrees.
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We know that angle π΄π΅πΆ is 43 degrees.
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Therefore, 43 plus angle π΅π΄π· is equal to 180.
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Subtracting 43 from both sides of this equation gives us π΅π΄π· is equal to 137.
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Therefore, the angle on the diagram π΅π΄π· is equal to 137 degrees.
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The question asked us to work out the bearing of π· from π΄.
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This is shown on the diagram by the pink arrow.
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Again, we must go clockwise from north.
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This angle is equal to 82 degrees plus 137 degrees.
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82 plus 137 is equal to 219.
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Therefore, the bearing of π· from π΄ is 219 degrees.
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We can check our answer is sensible by considering the four key points on a compass.
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If a point was due east, it would have a bearing of 90 degrees.
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If it was due south, 180 degrees and if it was due west, 270 degrees.
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On the map, it is clear that point π· is on a bearing from π΄ between south and west.
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Therefore, the answer must be between 180 and 270 degrees.
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This means that our answer of 219 degrees is sensible.