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Question
From the adjoining figure, find the value of x and y.
Sum
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Solution
Given:
- BC = 3x + 1
- DE = 16
- ∠B = 2y
- ∠E = 10°
Step-wise calculation:
Step 1: Use Congruence of Triangles
Since AB = AD, AC = AE and angle between them is equal.
⇒ ΔABC ≅ ΔADE
Therefore, corresponding parts of congruent triangles are equal (CPCTC).
Step 2: Use Corresponding Sides
From congruence:
BC = DE
⇒ 3x + 1 = 16
⇒ 3x = 15
⇒ x = 5
Step 3: Use Corresponding Angles
From congruence:
∠B = ∠E
⇒ 2y = 10°
⇒ y = 5
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