These are isosceles equatorial triangle questions

Step-by-step explanation:

1) ABCD rectangle

In Δ ABE

∠BAE +  ∠B + ∠AEB = 180 {angle sum property}

   39 + 90 + ∠AEB = 180

             129 + ∠AEB = 180

                       ∠AEB = 180 - 129

                      ∠AEB = 51

∠AEB + ∠AED + ∠CED = 180      {Straight line angles}

            51 + x + 66 = 180

              117 + x  = 180

                      x = 180 - 117

                    x = 63

2) XYZ  equilateral triangle

In equilateral triangle each angle = 60°

∠XZY = 60

∠XZY + ∠XZW = 180            {linear pair}

 60+ ∠XZW = 180

            ∠XZW = 180 - 60

∠XZW = 120

In ΔXZW,

120 + 35 +x = 180  {angle sum property of triangle}

        155 +x = 180

                 x = 180 - 155

                x = 25

PQR isosceles triangle

PQ = PR

∠PRQ = ∠Q =  69°

∠PRS + ∠PRQ = 180   {linear pair}

 ∠PRS + 69 = 180

        ∠PRS = 180 - 69

        ∠PRS = 111

In ΔPRS

x + 111 + 31 = 180         {Angle sum  property of triangle}

         x + 142 = 180

                x = 180 - 142

              x = 38