Question

the question answer is x = 22 and angle Q = 75 , Angle R = 105 and angle S = 55

Answer 1

PQRS is a quadrilateral.

∠P = 125°

∠Q = [ ( x + 8 ) + ( 2x + 1 ) ]°

∠R = [ 5 ( x - 1 ) ]°

∠S = [ ( x + 3 ) + 30 ]°

As we know that,

Sum of all angles of quadrilateral = 360°

•°•

∠P + ∠Q + ∠R + ∠S = 360°

Putting values, we get

125° + x + 8° + 2x + 1° + 5 ( x - 1 ) + x + 3° + 30° = 360°

Opening ( ) bracket

125° + x + 8° + 2x + 1° + 5x - 5° + x + 3° + 30° = 360°

162° + 9x = 360°

9x = 360° - 162°

9x = 198°

x = 22°

Now,

∠Q = x + 8 + 2x + 1 = 22 + 8 + 2 ( 22 ) + 1 = 75°

∠R = 5 ( x - 1 ) = 5 ( 22 - 1 ) = 105°

∠S = x + 3 + 30 = 22 + 33 = 55°