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Find the value of the unknown x in the following diagrams:
The sum of all interior angles of a triangle is 180°. By using this property, these problems can be solved as follows.
(i) x + 50° + 60° = 180°
x + 110° = 180°
x = 180° − 110° = 70°
(ii) x + 90° + 30° = 180°
x + 120° = 180°
x = 180° − 120° = 60°
(iii) x + 30° + 110° = 180°
x + 140° = 180°
x = 180° − 140° = 40°
(iv) 50° + x + x = 180°
50° + 2x = 180°
2x = 180° − 50° = 130°
(v) x + x + x = 180°
3x = 180°
(vi) x + 2x + 90° = 180°
3x = 180° − 90° = 90º
Find the value of the unknowns x and y in the following diagrams:
(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)
x + x + y = 180° (Angle sum property)
2x + y = 180°
2x + 90° = 180°
2x = 180° − 90° = 90°
(vi)
y = x (Vertically opposite angles)
a = 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°
Find the value of the unknown x in the following diagrams?
(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)
x + x + y = 180° (Angle sum property)
2x + y = 180°
2x + 90° = 180°
2x = 180° − 90° = 90°
(vi)
y = x (Vertically opposite angles)
a = 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°
Find the value of the unknowns x and y in the following diagrams?
The sum of all interior angles of a triangle is 180°. By using this property, these problems can be solved as follows.
(i) x + 50° + 60° = 180°
x + 110° = 180°
x = 180° − 110° = 70°
(ii) x + 90° + 30° = 180°
x + 120° = 180°
x = 180° − 120° = 60°
(iii) x + 30° + 110° = 180°
x + 140° = 180°
x = 180° − 140° = 40°
(iv) 50° + x + x = 180°
50° + 2x = 180°
2x = 180° − 50° = 130°
(v) x + x + x = 180°
3x = 180°
(vi) x + 2x + 90° = 180°
3x = 180° − 90° = 90º
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