# In Fig. 6.29, if AB || CD, CD || EF and y : z = 3 : 7, find x.

Fig. 6.29

**Solution:**

Given: AB || CD, CD || EF and y : z = 3 : 7

To find: The value of x

When two parallel lines are cut by a transversal, co-interior angles formed are supplementary.

Also, we know that lines which are parallel to the same line are parallel to each other.

Thus, If AB || CD, CD || EF, we can say AB || EF.

Therefore, the angles x and z are alternate interior angles and hence are equal.

x = z.......(1)

AB and CD are parallel lines cut by a transversal. So the co-interior angles formed are supplementary.

x + y = 180°.

Since x = z,

We get y + z = 180°......... (2)

Let, y = 3a, z = 7a [Since, y : z = 3 : 7]

Substituting the values in equation (2),

3a + 7a = 180°

10a = 180°

a = 180°/10

a = 18°

∴ y = 3a = 3 × 18 = 54°

y = 54°

∴ x + y = 180°

x + 54° = 180°

x = 180° - 54°

x = 126°

Thus, x = 126°

**Video Solution:**

## In Fig. 6.29, if AB || CD, CD || EF and y : z = 3 : 7, find x.

### NCERT Solutions Class 9 Maths - Chapter 6 Exercise 6.2 Question 2:

**Summary:**

If AB||CD, CD||EF and y : z = 3 : 7, then the value of x from the given figure is 126°.