Question

Given triangle PRS is congruent to triangle CFH, find the values of x , y and z ?

Answer 1

Answer:

x = 23

y = 7

z = 11

Step-by-step explanation:

Given ΔPRS ≅ ΔCFH

By CPCTC of these triangles,

m∠R = m∠F

(13y - 1)° = 90°

13y = 90 + 1

13y = 91

y = 7

Side PS ≅ Side CH

2x - 7 = 39

2x = 39 + 7

2x = 46

x = 23

∠H ≅ ∠S

m∠H = m∠S

Since, m∠P + m∠R + m∠S = 180°

m∠S = 180° - (m∠P + m∠R)

        = 180° - [28° + (13y - 1)]

        = (180 - 28) - (13y - 1)

        = 152 - (13y - 1)

Now, 152 - (13y - 1) = (6z - 4) [Since, m∠H = m∠S]

152 - (13×7 - 1) = 6z - 4 [Since, y = 7]

152 - 90 = 6z - 4

62 = 6z - 4

6z = 66

z = 11