Idon’t understand this. triangles abc and pqr are given. triangle abc is congruent to pqr by sas. if angle abc=12x+2, angle pqr= 142-2x,

The true statements:

- AB = 8

- x is seven units greater than y

- m∠ABC = 122°

Step-by-step explanation:

* One case of congruence is SAS that means

- If two sides and including angle between them in the first

 triangle equal to the corresponding sides and angle in the

 second triangle, then the two triangles are congruent

* In the problem

- Triangle ABC is congruent to triangle PQR using SAS case

* That means

- AB = PQ

- BC = QR

- m∠ABC = m∠PQR  

- Where angle ABC including angle between AB and BC

  and angle PQR is the including angle between PQ and QR

* Now we will use the information about the lengths of AB

 and PQ to find y, and use the measures of angles ABC and

 PQR to find x and then chose the correct answer

∵ m∠ABC = 12x + 2

∵ m∠PQR = 142 - 2x

∵ m∠ABC = m∠PQR

∴ 12x + 2 = 142 - 2x ⇒ collect the like terms

∴ 12x + 2x = 142 - 2

∴ 14 x = 140 ⇒ divide both sides by 14

∴ x = 10

* Lets substitute this value of x to find the m∠ABC and m∠PQR

- m∠ABC = 12(10) + 2 = 120 + 2 = 122°

- m∠PQR = 142 - 2(10) = 142 - 20 = 122°

∵ AB = 5y - 7

∵ PQ = 3y - 1

∵ AB = PQ

∴ 5y - 7 = 3y - 1 ⇒ collect the like terms

∴ 5y - 3y = -1 + 7

∴ 2y = 6 ⇒ divide both sides by 2

∴ y = 3

* Lets substitute this value of y to find the AB and PQ

- AB = 5(3) - 7 = 8 units

- PQ = 3(3) - 1 = 8 units

* Lets check the answer to chose the right answer

- 1st answer ⇒ AB = 8 (√)

- 2nd answer ⇒ m∠PQR = 140° (x)

- 3rd answer ⇒ y = 1 (x)

- 4th answer ⇒ x is seven units greater than y (√)

  ( x = 10 and y = 3 then x - y = 10 - 3 = 7)

- 5th answer ⇒ m∠ABC = 122° (√)

- 6th answer ⇒ PQ = 3 (x)

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068