Mathematics

In the following figure, find the values of x and y.

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

Triangles

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Answer

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

In △ABC and △CDE,

∠ACB = ∠DCE (Vertically opposite angles)

∠BAC = ∠CED (Given)

BC = CD (Given)

∴ △ABC ≅ △CDE (By AAS axiom)

We know that corresponding parts of congruent triangles are equal.

∴ DE = AB

⇒ 2y + 3 = 25

⇒ 2y = 22

⇒ y = 11.

Given, BC = CD

⇒ 3x - 7 = 32

⇒ 3x = 32 + 7

⇒ 3x = 39

⇒ x = 13.

Hence, x = 13 and y = 11.

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