Question

These are isosceles equatorial triangle questions

Answer 1

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