Download Angles 1. A whole turn Angles at a point add up to

4. Angles
Angles
1. A whole turn
Angles at a point add up to 360°
53° + 80° + 140° + 87° = 360°
2. A quarter of a turn
Right angle = 90◦
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3. A straight line
Angle on a straight line is equal to 180°
4. Acute Angles -
The acute angle is the angle which is less than 90°.
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5. Obtuse Angles
Obtuse angles are larger than 90° but smaller than 180°
Reflex Angles
Angles larger than 180° (straight line) are called reflex
angles.
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Drawing angles
This is a protractor; it helps you measure angles, in degrees:
Example: Construct and angle of 50°
Step 1: Draw a sketch
50◦
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Step2: Draw a straight line
Step 3: Put the centre of the protractor on the mark with
the start line and use a protractor and measure an angle of
50°
Step 3: Using a ruler draw a straight line.
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Step 4: Draw and arc and label the angle 50°
http://www.mathsisfun.com/geometry/protractorusing.html
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Constructing Triangles
s
Constructing ∆ given 2 sides (cm) and 1 angles (°)
Example:
Construct ∆ ABC, AB = 6.5 cm, AC = 7.5 cm and
Measure BC
1st step: Draw a sketch and label it.
C
A
50◦
B
6.5cm
2nd step: Draw a line of 6.5cm and name it AB
A
B
6.5cm
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A=50°.
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3rd step: Draw
A=50° and line AC = 7.5cm
C
7.5cm
A
6.5cm
B
4th Step: Draw line BC and measure BC
C
7.5cm
A
B
6.5cm
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Constructing
∆s given 1 side (cm) and 2 angles (°)
Construct ∆ XYZ, XY = 8cm,
X = 52° and
Y=64°.
1st step: Draw a sketch and label it.
Z
52◦
X
64◦
8cm
Y
2nd step: Draw a line of 8 cm and name it XY
X
3rd step: Draw
8cm
Y
X=52°
X
8cm
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Y
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4th step: Draw
Y=64°
Z
52◦
X
Z = 64◦
64◦
8cm
Y
Therefore, it is an isosceles triangle.
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Parallel lines
Lines are parallel if they are always the same distance apart.
They are called "equidistant", and will never meet.
Non-Parallel lines
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Angle calculations
Angles at a point add up to 360°
Adjacent angles
Angles on a straight line are called adjacent angles and add
up to 180°
Angles on a straight line add up to 180◦
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Corresponding angles
When two lines are crossed by another line (called
the Transversal):
Corresponding Angles are equal
Alternate angles (Angles found in a Z-shaped figure)
Angles are equal.
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Vertically opposite angles
Angles a and c are equal and also d and b are equal and are
called vertically opposite angles.
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Example: Find angles a and b
We can use the fact that angles around a point add up to 360°
Therefore, angle a is 360° - 270° = 90° Angle a = 90°
Angle b = 360° -180° - 30° = 150°
Angle b = 150°
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Example: Given the diagram below, determine the values of
the angles b, c, d, e, f, g and h.
Give angle facts.
Step 1: b = 180°-60°=120° (adj angles on a straight line)
Step 2: b and c are equal. (vertically opposite angles).
Therefore, c = b = 120°
Step 3: d and 60° are equal (vertically opposite angles).
Therefore, d = 60°
Step 4: d and e are equal. (alternate angles).
Therefore, e = d = 60°
Step 5: b and f are equal (corresponding angles).
Therefore, b = f=60°
Step 6: g and f are equal ( vertically opposite angles).
Therefore, g = f = 120°
Step 7: h and d are equal (corresponding angles).
Therefore, h = d = 60°
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