Question

in the adjoining figure,AB//BC . With the help of the given information find the value of x and y

please answer fast​

Answer 1

Answer:

• x = 24
• y = 54

GivEn :-

• In the adjoining fig. AB || BC
• ∠DAE = (x + 19)°
• ∠BAC = (2x + y)°
• ∠ABC = (y - 11)°
• ∠ACB = (x + 11)°

To Find :-

• value of x and y

Diagram :-

• Refer to the attachment

Step-by-step explanation:

As AB || BC, the similar angles, ∠DAE =∠ABC

➠ x + 19 = y - 11

➾ x - y = - 11 - 19 = ( - 30)............(i)

Now, we know that, the sum of three angles of a triangle = 180°

➠ ∠BAC + ∠ABC + ∠ACB = 180°

➾ 2x + y + y - 11 + x + 11 = 180

➾ 3x + 2y = 180.......................(ii)

➤ Now solving the two equations,

➥ 3x + 2y = 180

➥ 2x - 2y = - 60 (multiplying each by 2)

______________

➾ 5x = 120

➾ x = (120 ÷ 5) = 24

➤ Now, putting the value in equation (i),

➥ 24 - y = - 30

➾ y = 30 + 24 = 54

Hence, we get the answers!