Mathematics
Find the size of each lettered angle in the following figure:
Rectilinear Figures
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Answer
In given figure, AD || FE [Given]
⇒ 60° + y = 180° and x + 110° = 180° (∵ Sum of adjacent interior angle in trapezium = 180°)
⇒ y = 180° – 60° and x = 180° – 110°
⇒ y = 120° and x = 70°
Since, AB || DE [Given]
∠BAD = ∠ADE = 70° (Alternate angles are equal)
In quadrilateral ABCD,
⇒ ∠BAD + 75° + z + 130° = 360° (∵ Sum of angles of a quadrilateral = 360°)
⇒ 70° + 75° + z + 130° = 360°
⇒ 275° + z = 360°
⇒ z = 360° – 275° = 85°.
Hence, x = 70°, y = 120° and z = 85°.
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