Question

Ok need to find missing measurements for number 5

And need number 9 answered I have uploaded the homework problems
Thanks so much!

Answer 1

Explanation:

5) ΔGHJ ≅ ΔXYZ

ΔGHJ is an isosceles triangle. So, GH = JH

GH =JH = 27 ft

a) GJ =XZ

GJ = 18 ft

b) XY = GH

XY = 27 ft

c) ZY = JH

ZY = 27 ft

d) ∠H = ∠Y

∠H = 38

In ΔGHJ,

∠G = ∠J {Isosceles triangle property}

Let ∠G = ∠J = x

∠G + ∠H + ∠J = 180 {angle sum property of triangle}

x + 38 + x = 180

38 +2x = 180

2x = 180 - 38

2x = 142

x = 142/2

x = 71

∠G = ∠J = 71

e) ∠Z = ∠J

∠Z = 71

f) ∠J = 71

9) ΔQRS ≅ ΔMNP

QR = 11 ; QS =15

MP = 2x +1

MP = QS

2x + 1 = 15

2x = 15 - 1

2x = 14

x = 14/2

x = 7

m∠S = 84

m∠R = 32

m∠Q = 17y - 4

In ΔQRS,

m∠Q + m∠R + m∠S = 180 {Angle sum property of triangle}

17y - 4 + 32 + 84 = 180

17y + 112 = 180

17y = 180 - 112

17y = 68

y = 68/17

y = 4