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Find the value of the unknown x in the following diagrams?

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Learn Exercise 6.3

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(i) y + 120° = 180° (Linear pair) y = 180° − 120º = 60º x + y + 50° = 180° (Angle sum property) x + 60° + 50° = 180° x + 110° = 180° x = 180° − 110° = 70° (ii) y = 80° (Vertically opposite angles) y + x + 50° = 180°...
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(i) y + 120° = 180° (Linear pair)

y = 180° − 120º = 60º

x + y + 50° = 180° (Angle sum property)

x + 60° + 50° = 180°

x + 110° = 180°

x = 180° − 110° = 70°

(ii) y = 80° (Vertically opposite angles)

y + x + 50° = 180° (Angle sum property)

80° + x + 50° = 180°

x + 130º = 180°

x = 180° − 130º = 50°

(iii) y + 50° + 60° = 180° (Angle sum property)

y = 180° − 60° − 50° = 70°

x + y = 180° (Linear pair)

x = 180° − y = 180° − 70° = 110°

(iv) x = 60º (Vertically opposite angles)

30° + x + y = 180°

30° + 60° + y = 180°

y = 180° − 30° − 60° = 90°

(v) y = 90° (Vertically opposite angles)

y = 180° (Angle sum property)

2x + y = 180°

2x + 90° = 180°

2x = 180° − 90° = 90°

(vi)

y = x (Vertically opposite angles)

x (Vertically opposite angles)

b = x (Vertically opposite angles)

a + b + y = 180° (Angle sum property)

x + x + x = 180°

3x = 180°

y = x = 60°

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1) x=70-->180-(50+60)=70, 2)x=180-(90+30)=60 3)x=180-(110+30)=40 4)2x+50=180 5)3x=180 6)3x+90=180 2x=180-50 x=180/3 3x=180-90 2x=130 x=60 3x=90 x=130/2=65 x=90/3=30 2x=2*...
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1) x=70-->180-(50+60)=70, 2)x=180-(90+30)=60 3)x=180-(110+30)=40

4)2x+50=180     5)3x=180    6)3x+90=180

2x=180-50            x=180/3      3x=180-90

2x=130                 x=60            3x=90

x=130/2=65                              x=90/3=30

                                                 2x=2*30=60

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