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)