Question

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

Answer 1

✬ x + y = 180° ✬

Step-by-step explanation:

Given:

• x + y = w + z

To Prove:

• AOB is a line.

Proof: We know that the sum of all the angles around a point forms a Complete Angle (180°). Therefore,

➨ x + y + w + z = 360°

$\implies{\rm }$ (x + y) + (w + z) = 360°

$\implies{\rm }$ (x + y) + (x + y) = 360° [∵ x + y = w + z ]

$\implies{\rm }$ 2x + 2y = 360°

$\implies{\rm }$ 2(x + y) = 360°

$\implies{\rm }$ x + y = 360/2

$\implies{\rm }$ x + y = 180°

If the sum all angles formed on the same side on a straight line is of 180°. Then we can say that the line is Straight Line.

Here,

➟ x + y = 180°. Therefore the line is straight.

Hence Proved.

Answer 2

$\\ Given: \\ x + y = W + Z \\ To Prove: \\ AOB is a line. \\ Proof: We know that the sum of all the \: angles around a point \: forms a Complete \: Angle ( {180}^{o}). \\ Therefore, \\ - x + y + W + Z = {360}^{o} \\ = (x + y) + (W + z) = {360}^{o} \\ = (x + y) + (x + y) ={360}^{o} [:x+y=w+ z} \\ 2x + 2y = {360}^{o} \\ = 2(x + y) = {360}^{o} \\ = x + y = 360/2 \\ = x + y = {180}^{o}$