Question

Fig. 6.15
4. In Fig. 6.16, if x + y =w+z, then prove that AOB
is a line.
LA
D
Fig. 6.16​

Answer 1

Answer:

x+y+w+z =360

(x+y)+(x+y) = 360

2(x+y) = 360

x+y = 180

since,

w+z = x+y

w+z = 180

x+y = 180

From ' reverse linear pair axiom' AOB is a straight line.

Answer 2

Question :-

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

Answer :-

Sum of all the angles at a point = 360°

∴ x + y + z + w = 360° or, (x + y) + (z + w) = 360°

But (x + y) = (z + w) [Given]

∴ (x + y) + (x + y) = 360° or,

2(x + y) = 360°

or, (x + y) = 360° /2 = 180°

∴ AOB is a straight line.

Plz mrk as brainliest ❤