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If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.

Rectilinear Figures

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Answer

Let a parallelogram be ABCD.

If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Let ∠A = x and so adjacent angle (∠B) = 23x\dfrac{2}{3}x

As AD || BC, sum of co-int ∠s = 180°,

x+23x=180°3x+2x3=180°5x3=180°x=180°×35x=108°2x3=2×108°3=72°.\therefore x + \dfrac{2}{3}x = 180° \\[1em] \Rightarrow \dfrac{3x + 2x}{3} = 180° \\[1em] \Rightarrow \dfrac{5x}{3} = 180° \\[1em] \Rightarrow x = \dfrac{180° \times 3}{5} \\[1em] \Rightarrow x = 108° \\[1em] \Rightarrow \dfrac{2x}{3} = \dfrac{2 \times 108°}{3} = 72°.

Opposite angles of a parallelogram are equal.

∴ ∠C = ∠A = 108° and ∠D = ∠B = 72°

Hence, angles of parallelogram are 108°, 72°, 108° and 72°.

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