If two lines intersect, prove that the vertically opposite angles are equal.

Question

TextTheorem on Vertically Opposite AnglesNCERT Exemplar

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lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.

In Fig. 6.9, lines PQ and RS intersect each other at point O. If ∠ POR : ∠ ROQ = 5 : 7, find all the angles.

Theorem on Vertically Opposite Angles

In Fig. 6.13, lines AB and CD intersect at O. If ∠ AOC + ∠ BOE = 70° and ∠ BOD = 40°, find ∠ BOE and reflex ∠ COE.

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer.

In Fig. 6.7, AB, CD and EF are three lines concurrent at O. Find the value of y.