BD is the angle bisector of ZABC 5x-Y

2x+y

14+y

(x+13y

x=[ ? ]

Enter

x = 7, y = 2

Explanation:

Two triangles are said to be congruent if all three sides and three angles of one triangle is equal to three sides and three angles of the other triangle.

From the question:

BD ≅ BD (reflexive property of equality)

Since BD is the angle bisector of ∠ABC, hence ∠ABD = ∠CBD

∠ABD = 2x + y, ∠CBD = 14 + y. Therefore:

2x + y = 14 + y

2x = 14 + y - y

2x = 14

x = 14 / 2

x = 7

Also, ∠BAD = ∠BCD = 90° (right angled triangle)

Since ∠BAD = ∠BCD, BD ≅ BD and ∠ABD = ∠CBD, therefore ΔABD is congruent to ΔCBD by angle-angle-side congruence theorem.

The angle-angle-side congruence theorem states that if two angles and one side of one triangle is equal to two angles and one side of another triangle the both triangles are congruent.

ΔABD is congruent to ΔCBD, therefore AD = CD

5x - y = x + 13y

13y + y = 5x - x

14y = 4x

14y = 4(7)

y = 4(7) / 14

y = 2