Question

Find the value of the unknowns x and y in the following diagrams:

Answer 1

(i) \(y + 120° = 180° \)(Linear pair) 
\(y= 180° - 120\degree = 60\degree x + y + 50° = 180°\) (Angle sum property) \(x + 60° + 50°\) 
= \(180° x + 110° = 180° x\) 
= \(180° - 110° = 70°\)

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(ii) \(y = 80°\) (Vertically opposite angles) 
\(y + x + 50° = 180°\) (Angle sum property)
\(80° + x + 50° = 180° x + 130\degree = 180°\)
\(x = 180° - 130 º = 50°\)

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(iii) \(y + 50° + 60° = 180°\) (Angle sum property)
\(y = 180° - 60° - 50° = 70° x + y = 180°\)
(Linear pair) \(x = 180° - y = 180° - 70°\) 
= \(110°\)

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(iv) x = 60 º (Vertically opposite angles)
\(30° + x + y = 180° 30° + 60° + y =180° y = 180° - 30° - 60° = 90°\)

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(v) \(y = 90°\) (Vertically opposite angles) \(x + x +y = 180°\) (Angle sum property)
\(2x + y = 180° 2x+ 90° = 180°\)
\(x = \frac{90\degree}{2}=45\degree\)

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(vi)
 
\(y = x\) (Vertically opposite angles) \(a = x\) (Vertically opposite angles) \(b = x\) (Vertically opposite angles) \(a + b + y\) = \(180°\) (Angle sum property) \(x + x + x = 180°\)
\(3x = 180°\)
\(x = \frac{180\degree}{3}=60\degree\)
\(y = x = 60°\)