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