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Find the size of each lettered angle in the following figure.

Find the size of each lettered angle in the figure. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Rectilinear Figures

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Answer

Find the size of each lettered angle in the figure. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

As CDE is a straight line

∠ADE + ∠ADC = 180°

122° + ∠ADC = 180°

∠ADC = 180° – 122° = 58° … (i)

Internal ∠ABC = 360° – 140° = 220° … (ii)

Now, in quadrilateral ABCD we have

⇒ ∠ADC + ∠BCD + ∠BAD + ∠ABC = 360° (As sum of all angles in a quadrilateral is 360°.)

⇒ 58° + 53° + x + 220° = 360° [Using (i) and (ii)]

⇒ 331° + x = 360°

⇒ x = 360° – 331°

⇒ x = 29°

Hence, x = 29°

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