Question:medium

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

Updated On: Jan 20, 2026
Show Solution

Solution and Explanation

Given:
x + y = w + z

It is observed that:

\[ x + y + z + w = 360^\circ \]

It is given that:

\[ x + y = w + z \]

So, we can rewrite the equation as:

\[ (x + y) + (x + y) = 360^\circ \]

\[ 2(x + y) = 360^\circ \]

Therefore:

\[ (x + y) = 180^\circ \]

Since \( x \) and \( y \) form a linear pair, we can conclude that \( \angle AOB \) is a straight line.

Was this answer helpful?
2

Top Questions on Intersecting Lines and Non-intersecting Lines

Questions Asked in CBSE Class IX exam

(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find: 

(i) how many cross - streets can be referred to as (4, 3). 

(ii) how many cross - streets can be referred to as (3, 4).

View Solution