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प्रश्न
Line AB || line CD || line EF and line QP is their transversal. If y : z = 3 : 7 then find the measure of ∠x.
उत्तर
line AB || line EF ...(Given)
And the line QP is their transversal.
∴ ∠x ≅ ∠z ...(Alternate angles)
∠y : ∠z = 3 : 7 ...(Given)
∴ ∠y = ∠x = 3 : 7
Let m be a common multiple of the ratio 3 : 7.
∴ ∠y = 3m, ∠x = 7m
line AB || line CD ...(Given)
And the line QP is their transversal.
∴ ∠x + ∠y = 180° ...(interior angle theorem)
∴ 7m + 3m = 180°
∴ 10m = 180°
∴ m = `(180°)/10`
∴ m = 18°
∠x = 7m
∴ ∠x = 7 × 18°
∴ ∠x = 126°
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