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