Question

If two supplementary angles are in the ratio 7 : 11 . Find these angles.

Answer 1

7x + 11x =180

18x =180

x=10

7x =70

11x =110

Answer 2

Given that,

• Two supplementary angles are in the ratio 7 : 11.

❒ Let the supplementary angles be 7x and 11x.

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$\underline{\bf{\dag} \:\mathfrak{As \: we \: know \: that\: :}}$

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• Sum of supplementary angles is 180°.

Therefore,

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$:\implies\sf 7x + 11x = 180^{\circ} \\\\\\:\implies\sf 18x = 180^{\circ} \\\\\\:\implies\sf x = \cancel\dfrac{180^{\circ}}{18} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 10^{\circ}}}}}}\:\bigstar$

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Hence,

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• First angle, 7x = (7 × 10) = 70°
• Second angle, 11x = (11 × 10) = 110°.

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$\therefore\:{\underline{\sf{Hence, \ required\: angles \: are \: \bf{70^{\circ} \: and \: 110^{\circ}}.}}}$⠀⠀⠀