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.

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.

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

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