Question

In given the figures if AB ll CD, CD ll EF and y :z =3:7find x ​

Answer 1

Answer:

126

Step-by-step explanation:

Given y:z = 3:7

Let y = 3p and z = 7p

x and z are alternate interior angles

hence x = z

x = 7p

Now x and y are co-interior angles and hence their sum is 180

x + y = 180

7p + 3p = 180

10p = 180

p = 180/10

p = 18

hence the value of x is 7p = 7 × 18 = 126

Answer 2

★ Solution :-

In this question, we are given with three lines which all are parallel to each other. A line is passing through all of them. It's called as a transversal line.

In the figure attached in the master, there is an other angle marked with the variable y, which says us that both the angles named y are equal. First, we'll find the values of y and z.

The concept used to find the value of y and z is the concept called as 'The interior angles on the same side of the transversal always measures 180° totally'. So,

$\sf \leadsto \angle{y} + \angle{z} = {180}^{\circ}$

$\sf \leadsto 3 : 7 = {180}^{\circ}$

$\sf \leadsto 3x + 7x = {180}^{\circ}$

$\sf \leadsto 10x = {180}^{\circ}$

$\sf \leadsto x = \dfrac{180}{10}$

$\sf \leadsto x = 18$

Value of ∠y :-

$\sf \leadsto 3x = 3(18)$

$\sf \leadsto \angle{y} = {54}^{\circ}$

Value of ∠z :-

$\sf \leadsto 7x = 7(18)$

$\sf \leadsto \angle{z} = {126}^{\circ}$

Now, to find the value of the ∠x, we use the same concept which was used above i.e, 'The interior angles on the same side of the transversal always measures 180° totally'.

Value of ∠x :-

$\sf \leadsto \angle{x} + \angle{y} = {180}^{\circ}$

$\sf \leadsto \angle{x} + {54}^{\circ} = {180}^{\circ}$

$\sf \leadsto \angle{x} = 180 - 54$

$\sf \leadsto \angle{x} = {126}^{\circ}$

Therefore, the value of the ∠x is 126°.