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In the following figure, find the value of x:

In the figure, find the value of x. Triangles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Triangles

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Answer

In △ADC,

DC = CA (Given)

∴ ∠ADC = ∠CAD = a.

∠ADC + ∠DCA + ∠CAD = 180°

⇒ a + 56° + a = 180°

⇒ 2a = 180° - 56°

⇒ 2a = 124°

⇒ a = 62°.

In △ABD,

AD = BD (Given)

∴ ∠ABD = ∠DAB = (x - a)°

In △ABD,

∠ABD + ∠BDA + ∠DAB = 180°

⇒ (x - a)° + (180 - a)° + (x - a)° = 180°

⇒ 2x° - 3a° + 180° = 180°

⇒ 2x° - 3(62°) = 0

⇒ 2x° - 186° = 0

⇒ 2x° = 186°

⇒ x° = 93°

⇒ x = 93.

Hence, x = 93.

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