Mathematics

In figure (1) given below, ABCD is a trapezium. Find the values of x and y.

Rectilinear Figures

ICSE

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Answer

Sum of adjacent co-interior angles of a trapezium = 180° (As AB || DC)

∴ ∠A + ∠D = 180°

⇒ x + 20° + 2x + 10° = 180°

⇒ 3x + 30° = 180°

⇒ 3x = 150°

⇒ x = $\dfrac{150°}{3}$

⇒ x = 50°.

∴ ∠B + ∠C = 180°

⇒ 92° + y = 180°

⇒ y = 180° - 92° = 88°.

Hence, x = 50° and y = 88°.

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