Question

In the figure, the lines GH and IJ are parallel. If ∠1 = 108° and ∠2 = 123°, find the value of x, y and z

Answer 1

Given GH || IZ

∠1 = 108°

∠2 = 123°

∠1 + ∠KGH = 180° ...[linear pair]

108° + ∠KGH = 180°

108° + ∠KGH – 108° = 180° – 108°

∠KGH = 72°

∠KGH = x°  ...(corresponding angles if KG is a transversal)

∴ x° = 72°

Similarly

∠2 + ∠GHK = 180°  ...(∵ linear pair)

123° + ∠GHK = 180°

123° + ∠GHK – 123° = 180° – 123°

∠GHK = 57°

Again ∠GHK = y°  ...(corresponding angles if KH is a transversal)

y = 57°

x° + y° + z° = 180°  ...(sum of three angles of a triangle is 180°)

72° + 57° + z° = 180°

129° + z° = 180°

129° + z° – 129° = 180° – 129°

z = 51°

∴ x = 72°, y = 57°, z = 51°