Question -
Answer -
(i)
y = 100° (opposite angles of a parallelogram)
x + 100° = 180° (Adjacent angles of a parallelogram)
⇒ x = 180° – 100° = 80°
x = z = 80° (opposite angles of a parallelogram)
∴, x = 80°, y = 100° and z = 80°
(ii)
50° + x = 180° ⇒ x = 180° – 50° = 130° (Adjacent angles of a parallelogram) x = y = 130° (opposite angles of a parallelogram)
x = z = 130° (corresponding angle)
(iii)
x = 90° (vertical opposite angles)
x + y + 30° = 180° (angle sum property of a triangle)
⇒ 90° + y + 30° = 180°
⇒ y = 180° – 120° = 60°
also, y = z = 60° (alternate angles)
(iv)
z = 80° (corresponding angle) z = y = 80° (alternate angles) x + y = 180° (adjacent angles)
⇒ x + 80° = 180° ⇒ x = 180° – 80° = 100°
(v)
x=28o
y = 112o z = 28o