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

Question

KnowledgeBoat · Accepted Answer

We know that, Sum of all angles round a point is equal to 360°. ⇒ x + y + w + z = 360° ⇒ (x + y) + (w + z) = 360° As, x + y = w + z ⇒ (x + y) + (x + y) = 360° ⇒ 2(x + y) = 360° ⇒ (x + y) = = 180°. ⇒ x + y = 180° and w + z = 180°. Since the sum of adjacent angles, x and y with OA and OB as the non-common arms is 180° we can say that AOB is a straight line. Hence, proved that AOB is a straight line.

Mathematics

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

Lines & Angles

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