Question

From the adjoining figure, find the value of x and y.

Answer 1

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