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

1.	In given the figures if AB ll CD, CD ll EF and y :z =3:7find x
Answer» ★ 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°.

Answer»

★ 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°.