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Answer :

Since, x,y,w and z are angles at a single point,

x + y + w + z = \(360^\circ\)

But it is given that, x + y = w + z

\(\because \) x + y + x + y = \(360^\circ\)

\(\Rightarrow \) 2(x + y) = \(360^\circ\)

\(\Rightarrow \) (x + y) = \(180^\circ\)

Hence, by converse of linear pair axiom, it is proved that AOB is a straight line.

- In figure, lines AB and CD intersect at O. If \(\angle{AOC}\) + \(\angle{BOE}\) = \(70^\circ\) and \(\angle{BOD}\) = \(40^\circ\), find \(\angle{BOE}\) and reflex \(\angle{COE}\).
- In figure, lines XY and MN intersect at O. If \(\angle{POY}\) = \(90^\circ\) and a :b = 2:3. Find c.
- In figure,\(\angle{PQR}\) = \(\angle{PRQ}\), then prove that\(\angle{PQS}\) = \(\angle{PRT}\) .
- 5.In figure below, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that \(\angle{ROS}\) = \(\frac{1}{2} \) (\(\angle{QOS}\) - \(\angle{POS}\)).
- It is given that \(\angle{XYZ}\) = \(64^\circ\) and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects \(\angle{ZYP}\) , find \(\angle{XYQ}\) and reflex\(\angle{QYP}\).

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