Question

find the values of x and y for which the lines AD and BC become parallel.

Answer 1

Given that AD // BC (Given)

Property: Alternate angles

5y = 2x  --------------- [ 1 ]

Property: Adjacent angles on a straight line sum up to 180º

∠BAC = 180 - 5y - 30

∠BAC = 150 - 5y

Property: Sum of angles in a triangle is 180º

(150 - 5y) + 2x + (x - y) = 180

150 - 5y + 2x + x - y = 180

3x - 6y = 30

x - 2y = 10

x = 10 + 2y  --------------- [ 2 ]

Put the 2 equations together:

5y = 2x        --------------- [ 1 ]

x = 10 + 2y  --------------- [ 2 ]

Find y:

Sub [ 2 ] into [ 1 ]:

5y = 2x

5y = 2(10 + 2y)

5y = 20 + 4y

y = 20º ------------------ Sub into equation [ 2 ] to find x

Find x:

x = 10 + 2y

x = 10 + 2(20)

x = 50º

Answer: x = 50º and y = 20º

Answer 2

Answer:

x=50 and y= 20

Step-by-step explanation:

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