1.

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

Answer»

(i) x + 100° = 180° (Adjacent angles are supplementary) x = 80°

z = x = 80º(Opposite angles are equal)

y = 100° (Opposite angles are equal)

(ii) 50° + y = 180° (Adjacent angles are supplementary)

y = 130°

x = y = 130° (Opposite angles are equal)

z = x = 130º (Corresponding angles)

(iii) x = 90° (Vertically opposite angles)

x + y + 30° = 180° (Angle sum property of triangles) 120° + y = 180°

y = 60°

z = y = 60° (Alternate interior angles)

(iv) z = 80° (Corresponding angles)

y = 80° (Opposite angles are equal)

x+ y = 180° (Adjacent angles are supplementary)

x = 180° − 80° = 100°

(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)


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