Question

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

• A.
  64
• B.
  130
  
• C.
  65
• D.
  128

Answer 1

The correct option is A

64
$\angle PRS=\angle P+\angle Q\text{[Exterior angle is equal to the sum}\text{of two interior opposite angles]}\angle PRS=b+{50}^{\circ }Now,\angle UTR=(b+{50}^{\circ })+a\text{[Exterior angle is equal to the sum}\text{of two interior opposute angles]}\Rightarrow {115}^{\circ }=b+{50}^{\circ }+a\Rightarrow a+b={65}^{\circ }(1^{\circ },{64}^{\circ })(2^{\circ },{63}^{\circ })....({64}^{\circ },1^{\circ })$
Hence, option a is correct