in Fig.6.26, ifx + y = w + z, then prove th t AOB is a line.Pacal

1.	in Fig.6.26, ifx + y = w + z, then prove th t AOB is a line.Pacal
Answer» Linear pair of angles: If Non common arms of two adjacent angles forma line, then these angles are called linear pair of angles. Axiom- 1 If a ray stands on a line, then the sum of twoadjacent angles so formed is 180°i.e, the sum of the linear pair is 180°. Axiom-2 If the sum of two adjacent angles is 180° thenthe two non common arms of the angles form a line. The two axioms given above together are calledthe linear pair axioms. --------------------------------------------------------------------------------------------------- Solution: 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. Therefore, AOB is a straight line.please like the solution 👍 ✔️👍

Answer»

Linear pair of angles:

If Non common arms of two adjacent angles forma line, then these angles are called linear pair of angles.

Axiom- 1

If a ray stands on a line, then the sum of twoadjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

Axiom-2

If the sum of two adjacent angles is 180° thenthe two non common arms of the angles form a line.

The two axioms given above together are calledthe linear pair axioms.

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Solution:

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.

Therefore, AOB is a straight line.please like the solution 👍 ✔️👍

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