Question

two lines m and n are parallel. Find x and y in the diagram. ​

Answer 1

Step-by-step explanation:

hope it helps u dear..,

Answer 2

Value of x = $\frac{68}{34}$   and value of y = $\frac{124}{7}$

Step-by-step explanation:

$\textbf{\Large In case of quadrilateral made of parallel lines, the sum of } \\\textbf{\Large adjacent angles is = 180 degree }$

Let (15x + 4y)° = A

and (10x + 5y)° = B

So according to the above property of the parallel lines,

A + 80° = 180°  (because both lying on same line n)

and

B + 72° = 180°  (because both lying on same line m)

So, solving these two equations we get

A = 100° and

B = 108°

again putting the values of A and B as

(15x + 4y)° = 100°                                        (equation 1)

(10x + 5y)° = 108°                                        (equation 2)

on multiplying equation (1) by 2   and equation (2) by 3

(30x + 8y)° = 200°                                      

(30x + 15y)° = 324°    

and subtracting each other now

7y° = 124°

so

y = $\frac{124}{7}$

putting the value of y° in equation (1), we get

$15x + 4\times \frac{124}{7} = 100\\\\\text{Solving this equation , we get}$

$x= \frac{68}{35}$

$\textbf{\Large So the value of x = }\frac{68}{35}\\\\\textbf{\Large and the value of y= }\frac{124}{7}$