Q. 33.5( 10 Votes )

An exterior angle

Answer :

The diagram for the question is as -


Since QR is extended to a point S, PRS becomes the exterior angle of the ΔPQR.


It is given to us that an exterior angle of a triangle is 105°.


So, PRS = 105° - - - - (i)


It is known to us that -


If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.


The two interior opposite angles are RPQ and PQR.


So, - - - - (ii)


But, in the question it is given that the interior opposite angles are equal.


RPQ = PQR - - - - (iii)


Substituting equation (iii) in equation (ii), we get




Substituting equation (i) in the above equation, we get



RPQ =


From (iii), we have RPQ = PQR



Thus, each of these equal angles is . So, option (B) is correct.


Also, (Since, sum of all the angles of a triangle is 180°)


And, (By linear pair axiom)



PRQ = 75°


So, we have the angles as –


RPQ = , PQR = , PRQ = 75°, and PRS = 105°


Option (A) is not correct because



But, PRQ is not the exterior angle. So, each of the equal angles is not .


Option (C) is not correct because . But, this is not equal to the exterior angle, PRS, which is 105°. So, each of the equal angles is not equal to .


Option (D) is not correct because. The value of PRQ is 75° which is not the interior angle. Thus, not equal to the exterior angle. So, each of the equal angles is not equal to 75°.

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