Question

17. In the given figure, if a and b are natural numbers,
then the number of possible pairs for (a, b) is

(1)130
(2)64
(3)65
(4)128
Aakash Educational Services Limited
answer is -- 64
​

Answer 1

Given : a and b are natural numbers in given figure .  

To Find :  number of possible pairs for (a, b)  

Solution:

x = ∠PUT

115° = b + x   ( exterior angle of triangle = sum of opposite two  interior angles )

x =  50° + a   ( exterior angle of triangle = sum of opposite two  interior angles )

=> 115° =  50° + a + b

=> a + b = 65°

One of them can be selected in 64 ways

(1  to 64 )    - other is automatically defined  

Hence number of possible pairs for (a, b) is   64

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Answer 2

Answer:

64 is the right answer.......