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Vertically Opposite Angles

In the given ...

Question

In the given figure, lines PQ and RS intersect each other at point O. If ∠POR: ∠ROQ = 5 : 7, find all the angles.

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Solution

Let andbe and respectively.

Since, Ray stand on line.Thus, and form a linear pair.

Therefore, their sum must be equal to.

Or,

Thus,

Thus,

It is evident from the figure, thatand are vertically opposite angles.

And we know that vertically opposite angles are equal.

Therefore,

Similarly,and are vertically opposite angles.

And we know that vertically opposite angles are equal.

Therefore,

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Q. In the Fig. lines PQ and RS intersect each other at point O. If

∠ P O R : ∠ R O Q = 5 : 7

, Find all the angles.

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$If ∠ P O R : ∠ R O Q = 5 : 9,$
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