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

(i) ABCD is a parallelogram.

∠B = y (Opposite angles of a parallelogram are equal)
⇒ y = 100°

Also,
z + 100° = 180° (Adjacent angles of a parallelogram are supplementary)
⇒ z = 180° – 100° = 80°
x = z= 80°  [Opposite angles of a parallelogram]
Hence x = 80°, y = 100° and z = 80°

(ii) This figure is also a parallelogram

∠1=50°(Opposite angles of a parallelogram are equal)

∠1+z=180°(linear pair)

⇒ z = 180° – 50° =130°

Now,

x + 50° = 180° (Adjacent angles of a parallelogram are supplementary)

⇒ x= 180° – 500° = 130°

also, x=y=130°(Opposite angles of a parallelogram are equal)

Hence x = 130°, y = 130° and z = 130°

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

x+y+30°=180°(Angle sum property of a triangle)

⇒90°+y+30°=180°

⇒y = 60°

Also this figure is a parallelogram

So, y=z=60°(Alternate interior angles)

Hence x = 90°, y = 60° and z = 60°

(iv) This figure is a parallelogram

z = 80°(Corresponding angles)

y=80°(Opposite angles of a parallelogram are equal)

Also, x+80°=180°(Adjacent angles of a parallelogram are supplementary)

⇒x = 100°

Hence x =100°, y = 80° and z = 80°

(v) This figure is also a parallelogram

y=112°(Opposite angles of a parallelogram are equal)

Also, x+y+40°=180°(Angle sum property of a triangle)

⇒x+112°+40°=180°

⇒x = 28°

Also, x=z=28°(Alternate interior angles)

Hence x = 28°, y = 112° and z = 28°