Respuesta :

Answer:

x = 23

y = 7

z = 11

Step-by-step explanation:

From ΔPRS,

(13y - 1)° + 28° + m∠S = 180°

m∠S = 180° - (13y + 27)°

m∠S = (153 - 13y)°

Since, ΔPRS ≅ ΔCFH,

m∠R = m∠F

(13y - 1)° = 90°

13y = 91

y = 7

m∠H ≅ m∠S

(6z - 4)° = (153 - 13y)

6z = 153 - 13y + 4

6z = 157 - 13y

6z = 157 - 13(7) [Since, y = 7]

6z = 66

z = 11

PS ≅ CH

(2x - 7) = 39

2x = 46

x = 23

MrRoyal

Congruent triangles have equal corresponding sides and angle measures

The values of x, y and z are 23, 7 and 11

Because triangle PRS is congruent to triangle CFH, then we have the following congruence statements:

[tex]\angle P \cong \angle C[/tex]

[tex]\angle R \cong \angle F[/tex]

[tex]\angle S \cong \angle H[/tex]

The above highlights mean that:

[tex]\angle R \cong \angle F[/tex]

[tex]13y - 1 =90[/tex]

Add 1 to both sides

[tex]13y =91[/tex]

Divide both sides by 13

[tex]y =7[/tex]

Also, we have:

[tex]\angle S \cong \angle H[/tex]

[tex]90 - 28 = 6z - 4[/tex]

Add 4 to both sides

[tex]66 = 6z[/tex]

Divide both sides by 6

[tex]11 = z[/tex]

Rewrite as:

[tex]z = 11[/tex]

Also, we have:

[tex]PS \cong CH[/tex]

This gives

[tex]2x - 7 \cong 39[/tex]

Add 7 to both sides

[tex]2x = 46[/tex]

Divide both sides by 2

[tex]x = 23[/tex]

Hence, the values of x, y and z are 23, 7 and 11

Read more about congruent triangles at:

https://brainly.com/question/13705338

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