Answer :

Let us consider two straight lines PR and SQ intersecting at a common point O.

The question is just a twisted version of very simple question.

**Proof:**

We know that a right angle means that the angle is equal to 90°.

So, four right angles mean that the angle is equal to 4 × 90° which is equal to 360°.

Let ∠POQ = ∠1

∠QOR = ∠2

∠SOR = ∠3

∠POS = ∠4.

Now when we observe the above diagram, ray QO is perpendicular to line PR.

So ∠1 + ∠2 = 180°……… (i) [As they form linear pair that is sum of angles in a straight line is 180°]

Similarly ray RO is perpendicular to line SQ.

So ∠2 + ∠3 = 180°……… (ii) [As they form linear pair that is sum of angles in a straight line is 180°]

Now let us add equations (i) and (ii).

So, we get ∠1 + ∠2 + ∠3 + ∠4 = 180° + 180°

∠1 + ∠2 + ∠3 + ∠4 = 360°.

Hence all the angles sum up to four right angles that is 360°.

Hence it is proved that the sum of measurement of the four angles is four right angles.

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