Question

in figure if x+y=w+z then prove that AOB is a line​

Answer 1

As Given, x+y=w+z

To Prove: AOB is a line or x+y=180  

∘

 (linear pair.)

According to the question,

x+y+w+z=360  

∘

 ∣ Angles around a point.

(x+y)+(w+z)=360  

∘

 

(x+y)+(x+y)=360  

∘

 ∣ Given x+y=w+z

2(x+y)=360  

∘

 

(x+y)=180  

∘

 

Hence, x+y makes a linear pair.  

Therefore, AOB is a straight line.

Answer 2

to prove AOB is a line.....

x+y+w+z = 360.

x+y+x+y = 360 (x+y= w+z) given

2x+2y = 360

2(x+y)=360

x+y = 360/2

x+y= 180.....

hence proved....... AOB is a line