Question

note book m solve plz ​

Answer 1

Answer:

180 - x......1

180 - y ....2

since angle opposite to the longer side is larger

hence using equation 1 and 2

we can conclude that MP>NP

Answer 2

Solution :

This can be simply be solved by using exterior and property and Euclid's axioms .

Consider Euclid's parallel postulate .

This states that :

If two lines are drawn which intersect the third line in such a way that the sum of the interior angles on one side is less than two right angles ( i.e, 180° ) then the two lines must inevitably intersect each other on that side of extended far enough .

Now let us use this axiom here as a corollary .

Here ,two lines subtended from infinity intersect with a transversal , MN .

We can clearly observe that ;

Angle M ( ext ) + Angle N ( ext ) > 180°

Angle M ( ext ) = Angle N ( int ) + Angle P ......... (1)

Angle N ( ext ) = Angle M ( int ) + angle p .......... (2)

Subtracting (2) from (1) [ as Angle M > Angle N ]

=> Angle M (ext ) - Angle N ( ext ) = Angle N ( int ) - angle M ( int )

=> MP > NP

< as opposite angles are greater so this follows >

Hence Shown

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