Question

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Answer 1

Answer:

Linear pair of angles:

If Non common arms of two adjacent angles form

a line, then these angles are called linear pair of angles.

Axiom-1

If a ray stands on a line, then the sum of two

adjacent 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° then

the two non common arms of the angles form a line.

Given:

x + y = w + z

To Prove:

AOB is a line or

x + y = 180° (linear pair.)

Proof:

A/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.