Question

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

Answer 1

Given,

x + y = w + z

To Prove,

AOB is a line or

x + y = 180° (linear pair.)

Proof:

A.T.Q

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.

Hence, x + y makes a linear pair.Therefore, AOB is a straight line.

Answer 2

Answer:

we know that sum of all the angles is 360°

∴ x+y+w+z=360°

⇒(x+y)+(w+z)=360°

⇒(w+z)+(w+z)=360°                                                                         [∵ x+y=y+z]

⇒w+z=180°

∴∠AOB=180°

i.e, AOB is a line

HOPE IT HELPS AND PLS MARK AS BRAINLIEST!!!!!!!