Mathematics
In a pentagon ABCDE, AB is parallel to DC and ∠A : ∠E : ∠D = 3 : 4 : 5. Find angle E.
Rectilinear Figures
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Answer
By formula,
Sum of interior angles of an 'n' sided polygon = (2n - 4) × 90°.
Sum of interior angles of 5 sided polygon = [2 × 5 - 4] × 90°
= [10 - 4] × 90°
= 6 × 90°
= 540°.
We know that,
Sum of interior angles on the same side of transversal are supplementary.
∴ ∠B + ∠C = 180°.
Given,
∠A : ∠E : ∠D = 3 : 4 : 5
Let ∠A = 3x, ∠E = 4x and ∠D = 5x.
∴ ∠A + ∠B + ∠C + ∠D + ∠E = 540°
⇒ 3x + 180° + 5x + 4x = 540°
⇒ 12x = 540° - 180°
⇒ 12x = 360°
⇒ x = = 30°.
⇒ ∠E = 4x = 4(30°) = 120°.
Hence, ∠E = 120°.
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