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) $x + x + x = 180°$
$3x = 180°$
$x = \frac{180\degree}{3}=60\degree$
$y = x = 60°$