Question

Please answer the question​

Answer 1

Given that a:b = 5:12

=> a / b = 5/ 12

=> a = 5b/12 (1)

And we have been given that ∆SQR is an equilateral triangle,so the value of b = 60°

=> a = 5 × 60/12

=> a = 5 × 5

=> a = 25°

Next we given that,c : d = 1:3

=> c/d = 1/3

=> c = d/3

=> c = 60/3 [ given that d = 60°)

=> c = 20° (2)

Now using all these results,we will find the angle QPR. In ∆PQR,

=> ∠QPR + (a + b) + (c + d) = 180°

From (1) and (2) we know the value of a and c and from the question we know the value of b and d,

=> ∠QPR + 25 + 60 + 20 + 60 = 180°

=> ∠QPR + 120 + 45 = 180

=> ∠QPR = 180 - 165

=> ∠QPR = 15°

Now,we will subtract ∠QSR from ∠QPR to obtain the result. We already know that ∠QSR = 60° because given that the ∆SQR is an equilateral triangle.

=> ∠QSR - ∠QPR

=> 60° - 15°

=> 45°

Therefore the answer of this question is 45°.