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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