1 / 37

Measuring angles

Measuring angles. An angle is a measure of turn and is usually measured in degrees. A full turn measures 360 °. 360 °. Measuring angles. An angle is a measure of turn and is usually measured in degrees. A half turn measures 180 °. This is a straight line. 180 °. Measuring angles.

gates
Télécharger la présentation

Measuring angles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Measuring angles An angle is a measure of turn and is usually measured in degrees. A full turn measures 360°. 360°

  2. Measuring angles An angle is a measure of turn and is usually measured in degrees. A half turn measures 180°. This is a straight line. 180°

  3. Measuring angles An angle is a measure of turn and is usually measured in degrees. A quarter turn measures 90°. It is called a right angle. 90° We label a right angle with a small square.

  4. Measuring angles An angle is a measure of turn and is usually measured in degrees. A three-quarter turn measures 270°. 270°

  5. Acute, obtuse and reflex angles An acute angle is between 0º and 90º. An obtuse angle is between 90º and 180º. An reflex angle is between 180º and 360º. All angles are acute, obtuse or reflex.

  6. Acute, obtuse and reflex angles Look at each interior angle in this shape. Is it acute, obtuse or reflex? B D C A I F E H G

  7. Using a protractor We measure angles with a protractor. Notice that the protractor has two scales. Before you measure an angle decide whether it is acute or obtuse.

  8. Labelling angles or ABC or B. The angle can then be described as ABC When two lines meet at a point an angle is formed. A B C An angle is a measure of the rotation of one of the line segments relative to the other. We label points using capital letters. Sometimes instead an angle is labelled with a lower case letter.

  9. Angles on a straight line Angles on a line add up to 180. a b a + b = 180° because there are 180° in a half turn.

  10. Angles in a triangle c a b For any triangle, a + b + c = 180° The angles in a triangle add up to 180°.

  11. Vertically opposite angles a d b c When two lines intersect, two pairs of vertically opposite angles are formed. and a = c b = d Vertically opposite angles are equal.

  12. Angles around a point Angles around a point add up to 360. b a c d a + b + c + d = 360 because there are 360 in a full turn.

  13. Complementary angles When two angles add up to 90° they are called complementary angles. a b a + b = 90° Angle a and angle b are complementary angles.

  14. Supplementary angles When two angles add up to 180° they are called supplementary angles. b a a + b = 180° Angle a and angle b are supplementary angles.

  15. Corresponding angles There are four pairs of corresponding angles, or F-angles. a a b b d d c c e e f f h h g g d = h because Corresponding angles are equal

  16. Corresponding angles There are four pairs of corresponding angles, or F-angles. a a b b d d c c e e f f h h g g a = e because Corresponding angles are equal

  17. Corresponding angles There are four pairs of corresponding angles, or F-angles. a b d c c e f h g g c = g because Corresponding angles are equal

  18. Corresponding angles There are four pairs of corresponding angles, or F-angles. a b b d c e f f h g b = f because Corresponding angles are equal

  19. Alternate angles There are two pairs of alternate angles, or Z-angles. a b d d c e f f h g d = f because Alternate angles are equal

  20. Alternate angles There are two pairs of alternate angles, or Z-angles. a b d c c e e f h g c = e because Alternate angles are equal

  21. Angles in an isosceles triangle In an isosceles triangle, two of the sides are equal. We indicate the equal sides by drawing dashes on them. The two angles at the bottom on the equal sides are called base angles. The two base angles are also equal. If we are told one angle in an isosceles triangle we can work out the other two.

  22. Exterior angles in polygons When we extend the sides of a polygon outside the shape exterior angles are formed. e d f

  23. Sum of the interior angles in a quadrilateral What is the sum of the interior angles in a quadrilateral? d c f a e b We can work this out by dividing the quadrilateral into two triangles. a + b + c = 180° and d + e + f = 180° So, (a + b + c)+ (d + e + f )= 360° The sum of the interior angles in a quadrilateral is 360°.

  24. Sum of interior angles in a polygon We have just shown that the sum of the interior angles in any quadrilateral is 360°. d a c b We already know that the sum of the interior angles in any triangle is 180°. c a + b + c = 180 ° a b a + b + c + d = 360 ° Do you know the sum of the interior angles for any other polygons?

  25. Sum of the interior angles in a pentagon What is the sum of the interior angles in a pentagon? c d a f g b e i h We can work this out by using lines from one vertex to divide the pentagon into three triangles . a + b + c = 180° and d + e + f = 180° and g + h + i = 180° So, (a + b + c)+ (d + e + f ) + (g + h + i) = 560° The sum of the interior angles in a pentagon is 560°.

  26. Sum of the interior angles in a polygon We’ve seen that a quadrilateral can be divided into two triangles … … and a pentagon can be divided into three triangles. A hexagon can be divided into four triangles. How many triangles can a hexagon be divided into?

  27. Sum of the interior angles in a polygon The number of triangles that a polygon can be divided into is always two less than the number of sides. We can say that: A polygon with n sides can be divided into (n – 2) triangles. The sum of the interior angles in a triangle is 180°. So, The sum of the interior angles in an n-sided polygon is (n – 2) × 180°.

  28. Interior angles in regular polygons A regular polygon has equal sides and equal angles. We can work out the size of the interior angles in a regular polygon as follows: Equilateral triangle 180° 180° ÷ 3 = 60° Square 2 × 180° = 360° 360° ÷ 4 = 90° Regular pentagon 3 × 180° = 540° 540° ÷ 5 = 108° Regular hexagon 4 × 180° = 720° 720° ÷ 6 = 120°

  29. Interior and exterior angles in an equilateral triangle 120° 60° 120° 60° 60° 120° In an equilateral triangle, Every interior angle measures 60°. Every exterior angle measures 120°. The sum of the interior angles is 3 × 60° = 180°. The sum of the exterior angles is 3 × 120° = 360°.

  30. Interior and exterior angles in a square 90° 90° 90° 90° 90° 90° 90° 90° In a square, Every interior angle measures 90°. Every exterior angle measures 90°. The sum of the interior angles is 4 × 90° = 360°. The sum of the exterior angles is 4 × 90° = 360°.

  31. Interior and exterior angles in a regular pentagon 72° 72° 108° 108° 108° 72° 108° 108° 72° 72° In a regular pentagon, Every interior angle measures 108°. Every exterior angle measures 72°. The sum of the interior angles is 5 × 108° = 540°. The sum of the exterior angles is 5 × 72° = 360°.

  32. Interior and exterior angles in a regular hexagon 60° 60° 60° 120° 120° 120° 120° 60° 120° 120° 60° 60° In a regular hexagon, Every interior angle measures 120°. Every exterior angle measures 60°. The sum of the interior angles is 6 × 120° = 720°. The sum of the exterior angles is 6 × 60° = 360°.

  33. The sum of exterior angles in a polygon For any polygon, the sum of the interior and exterior angles at each vertex is 180°. For n vertices, the sum of n interior and n exterior angles is n × 180° or 180n°. The sum of the interior angles is (n – 2) × 180°. 180n° – 360°. We can write this algebraically as 180(n – 2)° =

  34. The sum of exterior angles in a polygon If the sum of both the interior and the exterior angles is 180n° and the sum of the interior angles is 180n° – 360°, the sum of the exterior angles is the difference between these two. The sum of the exterior angles = 180n° – (180n° – 360°) = 180n° – 180n° + 360° = 360° The sum of the exterior angles in a polygon is 360°.

  35. Bearings N 75° P Bearings are a measure of direction taken from North. If you were travelling North you would be travelling on a bearing of 000°. If you were travelling from the point P in the direction shown by the arrow then you would be travelling on a bearing of 000°. If you were travelling from the point P in the direction shown by the arrow then you would be travelling on a bearing of 075°. Bearings are always measured clockwise from North and are written as three figures.

  36. Compass points 000° N 045° 315° NW NE E 270° W 090° SW SE 225° 135° S 180°

  37. Bearings N N 105º A B The bearing from point A to point B is 105º. What is the bearing from point B to point A? The angle from B to A is 105º + 180º = 285º This is called a reciprocal bearing or back bearing. ? 105º 180°

More Related