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Angle Facts

Angle Facts. Objectives: F Grade Express fractions of full turns in degrees and vice versa Recognise acute, obtuse, reflex and right angles Estimate angles and measure them accurately Use properties of angles at a point and angles on a straight line

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Angle Facts

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  1. Angle Facts Objectives: F Grade Express fractions of full turns in degrees and vice versa Recognise acute, obtuse, reflex and right angles Estimate angles and measure them accurately Use properties of angles at a point and angles on a straight line Understand the terms ‘perpendicular lines and ‘parallel lines’ D Grade Recognise corresponding angles and alternate angles

  2. Two lines at right angles (90o) to each other Straight lines that are always the same distance apart and never meet Angle Facts Define: Perpendicular Lines Define: Parallel

  3. Angle Facts Starter: Name these angles: Acute Obtuse Right Angle Reflex

  4. Vertical 2 1 Horizontal 90 90 90 90 4 3 Angles at a Point 360o 360o 360o 360o 360o

  5. d a c b Angles at a point add to 360o Angle a + b + c + d = 3600 Angles at a Point

  6. Example: Find angle a. 90 90 90 90 a 75o 85o 360o 80o 85 75 + 80 240 Angles at a Point Angle a = 360 - (85 + 75 + 80) = 360 - 240 = 120o

  7. d a c b Angles at a Point Opposite Angles are equal Angle a + b = 1800 because they form a straight line Angle c + d = 1800 because they form a straight line Angle c + b = 1800 because they form a straight line Angle d + a = 1800 because they form a straight line So a = c and b = d

  8. Angles on a straight line add to 180o 90 90 Angles a + b = 180o 180o a b Horizontal line x 70o b 35o Angles on a Line Oblique line Angle x = 180 – 35 = 145o Angle b = 180 – 70 = 110o

  9. Now do these: 110o f 35o a 120o 22o 45o b 60o 116o g d g g c 148o e i . h 80o h = 49.3 2h 135o Angle Facts f = 360 – (45+120+110) f = 360 - 275 = 85o a = 180 – 35 = 145o b = 180 – (22+90) = 68o 3g = 360 – (90+60) = 210 g = 70 Opposite angles are equal So c = 116o d = 180 – 116 = 64o i = 180 - 148 = 32o 3h = 180 – i = 148 e = 360 – (135+80) = 145o

  10. Transversal Angles between Parallel Lines Draw a pair of parallel lines with a transversal and measure the 8 angles. Parallel lines remain the same distance apart. Vertically opposite angles are equal. Corresponding angles are equal.

  11. Transversal Angles between Parallel Lines Draw a pair of parallel lines with a transversal and measure the 8 angles. Parallel lines remain the same distance apart. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal.

  12. Transversal Angles between Parallel Lines Draw a pair of parallel lines with a transversal and measure the 8 angles. Parallel lines remain the same distance apart. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  13. Angles between Parallel Lines

  14. Angles between Parallel Lines

  15. Transversal Angles between Parallel Lines Name an angle corresponding to the marked angle. a d c Parallel lines remain the same distance apart. e f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  16. Transversal Angles between Parallel Lines Name an angle corresponding to the marked angle. a b c Parallel lines remain the same distance apart. e f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  17. Transversal Angles between Parallel Lines Name an angle corresponding to the marked angle. a b d c Parallel lines remain the same distance apart. f g h Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  18. Transversal Angles between Parallel Lines Name an angle corresponding to the marked angle. a b d Parallel lines remain the same distance apart. e f g h Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  19. Transversal Angles between Parallel Lines Name an angle alternate to the marked angle. a b d Parallel lines remain the same distance apart. e f g h Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  20. Transversal Angles between Parallel Lines Name an angle alternate to the marked angle. a b d c Parallel lines remain the same distance apart. e g h Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  21. Transversal Angles between Parallel Lines Name an angle interior to the marked angle. a b c Parallel lines remain the same distance apart. d e g h Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  22. Transversal Angles between Parallel Lines Name an angle interior to the marked angle. a b d c Parallel lines remain the same distance apart. e g h Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  23. Angles between Parallel Lines d a h e c g f Name an angle corresponding to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  24. Angles between Parallel Lines d a e c b g f Name an angle alternate to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  25. Angles between Parallel Lines d h e c b g f Name an angle interior to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  26. Angles between Parallel Lines Name in order, the angles that are alternate,interior and corresponding to the marked angle. e h f g d b c Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  27. Angles between Parallel Lines Name in order, the angles that are alternate,interior and corresponding to the marked angle. d a c h e g f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  28. 80o Int. s 60o vert.opp. s 120o Int. s Angles between Parallel Lines Finding unknown angles  x =  y =  z = Find the unknown angles stating reasons, from the list below. z 100o y x 60o Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  29. 105o corr. s 55o alt. s 125o Int. s Angles between Parallel Lines Finding unknown angles  x =  y =  z = 105o 55o Find the unknown angles stating reasons, from the list below. z y x Vertically opposite angles are equal. vert.opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180o .(Supplementary) Int. s

  30.  x = 85o Int. s  y = 120o Int. s Angles between Parallel Lines Finding unknown angles Unknown angles in quadrilaterals and other figures can be found using these properties. Find the unknown angles stating reasons, from the list below. y 95o x 60o Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  31. 125o Int. s 55o Int. s 125o Int. s 55o 125o 125o Angles between Parallel Lines  x = Finding unknown angles  y = Unknown angles in quadrilaterals and other figures can be found using these properties.  z = y x Find the unknown angles stating reasons, from the list below. 55o z What does this tell you about parallelograms? Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)

  32.  a =  b =  c = 58o vert.opp. s  d = 32o s in tri  e = 52o 64o 58o 64o 58o 32o corr. s alt. s isos tri isos tri s on line s at a point  f =  g =  h = Angles between Parallel Lines 58o b a c e g f d 70o Mixing it! h Vertically opposite angles are equal. Find the unknown angles stating reasons, from the list below. There may be more than one reason. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angle sum of a triangle (180o) Angle on a line sum to(180o) Base angles isosceles triangle equal. Angles at a point sum to 360o

  33. Angle Facts 54o 99o Now do these: t w u v 65o 130o p x 38o q y r 77o 35o s z 48o t = 99o u = 81o v = 54o w = 126o Corresponding angles p = 65o x = 130o Alternate angles q = 38o y = 130o Corresponding angles r = 77o Opposite angles (with r) or Alternate angles with 77o s = 77o z = 35o + 48o = 83o

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