Question

Consider the following parallelograms. Find the values of the unknowns $x, y, z$.

Answer 1

(i) $x + 100° = 180°$ (Adjacent angles are supplementary)
$x = 80°$
$z = x = 80\degree$ (Opposite angles are equal)
$y = 100°$ (Opposite angles are equal)

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(ii) $50° + y = 180°$ (Adjacent angles are supplementary)
$y = 130°$
$x = y = 130°$ (Opposite angles are equal)
$z = x = 130\degree$ (Corresponding angles)

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(iii) $x = 90°$ (Vertically opposite angles)
$x + y + 30\degree = 180\degree$ (Angle sum property of triangles)
$120° + y = 180°$
$y = 60°$
$z = y = 60°$ (Alternate interior angles)

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(iv) $z = 80°$ (Corresponding angles)
$y = 80°$ (Opposite angles are equal)
$x+ y = 180°$ (Adjacent angles are supplementary)
$x = 180° - 80° = 100°$

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(v) $y = 112°$ (Opposite angles are equal)
$x+ y + 40° = 180°$ (Angle sum property of triangles)
$x + 112° + 40° = 180°$
$x + 152° = 180°$
$x = 28°$
$z = x = 28°$ (Alternate interior angles)