Answer:
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
