In the figure AB BC and DB BE A x degree C 4y degree D

In the figure, AB = BC and DB = BE, A = x degree, C = 4y degree, D = 4x - 5 degree and E = 15 y degree. (a) How are the triangles related? (b) Find x, y, A, C, D and E.

Solution

Solution:

(a)

In triangle ABE and triangle CBD

angle < ABE = angle < CDB ( vertically opposite angle)

BE = BD ( Given)

AB = CB ( Given)

therefore trinagle ABE and triangle CDB are congruents to each other by SAS

(b)

In both triangle

<A = <C

x = 4y

Now in both trinagle trinagle

x+15y +<B = 180 = 4x-5+4y +<B

x+15y = 4x+4y -5

3x -11y =5

as we know that 4x = y

12y -11y = 5

y= 5 and x = 20

<A = 20 , <C = 20 , <D = 75 and E = 75