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Types of Angle

1. 3. 2. Types of Angle. Acute angles. Acute angles are angles less than 90 o. 90 o on a protractor. Vertical. Horizontal. Horizontal. Horizontal. 1. 2. 3. Vertical. Vertical. Vertical. Horizontal. Types of Angle. Right angles.

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Types of Angle

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  1. 1 3 2 Types of Angle Acute angles Acute angles are angles less than 90o

  2. 90o on a protractor Vertical Horizontal Horizontal Horizontal 1 2 3 Vertical Vertical Vertical Horizontal Types of Angle Right angles If the angle between two lines is a right angle then the lines are perpendicular to each other. A right angle will occur when a horizontal line and a vertical line meet. A right angle is an angle of 90o

  3. Right angles Vertical Perpendicular lines Horizontal Perpendicular lines Types of Angle

  4. Which simple shapes contain right-angles?

  5. 5 8 6 five Eight six Can Pentagons, Hexagons and Octagons have right-angles? Regular Hexagon Regular Pentagon Regular Octagon Irregular Octagon Irregular Pentagon Irregular Hexagon

  6. 1 3 2 Types of Angle Obtuse angles Obtuse angles are greater than 90obut less 180o

  7. What types of angle can you see in the shapes below? 5 8 6 five Eight six Regular Hexagon Regular Pentagon Regular Octagon Irregular Octagon Irregular Pentagon Irregular Hexagon

  8. 180o on a protractor 180o on a protractor Types of Angle Straight angles A straight angle is an angle of 180o

  9. 1 4 2 3 Types of Angle Reflex angles Reflex angles are greater than 180obut less than 360o

  10. 1 3 2 4 5 6 7 9 8 Acute Acute Obtuse Right Obtuse Reflex Obtuse Acute Reflex

  11. Inside scale from 0o to 180o going in an anti-clockwise direction. Outside scale from 0o to 180o going in a clockwise direction. A 180o Protractor

  12. You need to be able to measure an angle to the nearest degree. To help you do this you should always: 1. Look directly down onto the cross point to improve accuracy. 2. Always use the protractor in a horizontal manner as shown below. 

  13. 1 0 on the inside so use inside scale 2 0 on the outside so use outside scale Measuring Angles with a 180o Protractor 50o 67o

  14. 3 4 0 on the inside so use inside scale 0 on the outside so use outside scale Measuring Angles with a 180o Protractor 120o 135o

  15. Measure each angle in the shapes below. 900 2 3 1 670 670 680 900 900 1120 680 900 460 1120 6 5 4 480 1180 730 1070 900 1010 1010 420 1100 1100 1070 730 Rectangle 3600 Trapezium 3600 Triangle 1800 Parallelogram 3600 Triangle 1800 Pentagon 5400

  16. 1 2 4 3 6 5 Estimating Angles

  17. 1 2

  18. 3 4

  19. Measure each angle in the shapes below. 2 3 1 6 5 4

  20. When a vertical line and a horizontal line meet the angle between them is 90o, a right angle. This angle is also a right angle. 90o, a right angle 90 90 Angles on a Line Vertical line Horizontal line This explains why the angles on a straight line add to 180o. The lines are said to be perpendicular to each other.

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

  22. Find the unknown angles 1 2 y 114o 47o x 3 4 82o b a 76o Angle y = 180 – 114 = 66o Angle x = 180 – 47 = 133o Angle b = 180 – 82 = 98o Angle a = 180 – 76 = 104o

  23. Vertical Remember: Angles at a on a line add to 180o Horizontal 90 90 Angles at a Point 90 90 This diagram helps explains why angles at a point add to 360o.

  24. Vertical 2 1 Horizontal 90 90 90 90 4 3 Angles at a Point 360o 360o 360o This explains why angles at a point add to 360o. 360o 360o

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

  26. Angles at a Point Example 1: Find angle a. 90 90 90 90 a 75o 85o 360o 80o 85 75 + 80 240 Angle a = 360 - (85 + 75 + 80) = 360 - 240 = 120o

  27. Angles at a Point Example 2: Find angle x. 90 90 90 90 105o x 360o 100o 90 100 + 105 295 Angle x = 360 - (90 + 100 + 105) = 360 - 295 = 65o

  28. 1 90o 360o 2 4 270o 180o 360o in a circle. What does it mean? 3

  29. Types of Triangles Scalene triangle Isosceles triangle Equilateral Triangle 3 equal sides 3 equal angles. 2 equal sides 2 equal angles (base) 3 unequal sides 3 unequal angles Angles In Triangles

  30. Any triangle containing a 90o angle is a right-angled triangle An isosceles or a scalene triangle may contain a right angle. Right-angled isosceles triangles. Right-angled scalene triangle.

  31. To determine the angle sum of any Triangle 3 1 2 Angles on a straight line add to 180o How can we use this to help us? Take 3 identical copies of this triangle like so: These are the same angles as in the triangle! The angle sum of a triangle = 1800

  32. Example 1 65o Calculate angle a. a Example 2 b Calculate angles a, b and c a c Calculating unknown Angles Angle a = 180 – (90 + 65) = 180 – 155 = 25o Since the triangle is equilateral, angles a, b and c are all 60o (180/3)

  33. Example 3 b Calculate angle a. a 65o Example 4 130o y Calculate angles x and y x Calculating unknown Angles Angle a = 65o (base angles of an isosceles triangle are equal). Angle b = 180 –(65 + 65) = 180 – 130 = 50o

  34. Example 5 Calculate angles a and b. a b Example 6 27o Calculate angle a a 15o Calculating unknown Angles Angle a = 180 – (15 + 27) = 180 – 42 = 138o

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