# In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.

**Solution:**

Given: x + y = w + z

To prove: AOB is a line.

We know that if the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.

From the figure we can see that,

(x + y) + (w + z) = 360° (complete angle)

It is given that (x + y) = (w + z),

Hence (x + y) + (w + z) = 360° can be written as (x + y) + (x + y) = 360°

2x + 2y = 360°

2(x + y) = 360°

x + y = 360°/2 = 180°

Since the sum of adjacent angles, x and y with OA and OB as the non-common arms is 180° we can say that AOB is a line.

**Video Solution:**

## In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.

### NCERT Solutions Class 9 Maths - Chapter 6 Exercise 6.1 Question 4:

**Summary:**

In Fig. 6.16, given that x + y = w + z, thus we have proved that AOB is a line as the sum of adjacent angles, x and y with OA and OB as the non-common arms is 180°.