Q. 11

# If two straight l

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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