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

(i)

(ii)

(iii)

(iv)

(v)

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

x = 80°

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

y = 100° (Opposite angles are equal)

(ii) x, y and z will be complimentary to 50⁰

Hence, required angle = 180 -50

= 130⁰

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

z = x = 130^o (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 in a parallelogram)

x+ y + 40° = 180° (Angle sum property of triangles)

x + 112° + 40° = 180°

x + 152° = 180°

x = 28°

z = x = 28° (Alternate interior angles)