Question

30°





Find the values of x, y for which the lines AD
and BC become parallel.
​

Answer 1

Step-by-step explanation:

Given that AD // BC (Given)

Property: Alternate angles

5y = 2x--------------------[1]

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

ZBAC = 180 - 5y - 30

ZBAC = 150 - 5y

Property: Sum of angles in a triangle is 180°

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

3x - 5y = 30

X - 2y = 10

x= 10 + 2y----------------[2]

Put the 2 equations together:

5y = 2x

x = 10 + 2y

Find y:

Sub [ 2 ] into [1]

5y = 2x

5y = 2(10 + 2y)

5y = 20 + 4y

y= 20°

to find x

Find x:

sub equation 1 & 2

x = 10 + 2y

x = 10 + 2(20)

x = 50°

Answer: x = 50° and y = 20°

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