Answer:
See below ~
Step-by-step explanation:
Solving for x in ΔLMN
- 6x + 3 + 4x - 10 + 5x + 7 = 180
- 15x = 180
- x = 12
Angles in ΔLMN
- (6x + 3)° = 6(12) + 3 = 75°
- (4x - 10)° = 4(12) - 10 = 38°
- (5x + 7)° = 5(12) + 7 = 67°
Solving for y in ΔSTU
- 5x + 3y + 9y - 7 + 6x - 5 = 180
- 11x + 12y - 12 = 180
- 11(12) + 12y = 192
- 132 + 12y = 192
- 12y = 60
- y = 5
Angles in ΔSTU
- (5x + 3y)° = 5(12) + 3(5) = 60 + 15 = 75°
- (9y - 7)° = 9(5) - 7 = 45 - 7 = 38°
- (6x - 5)° = 6(12) - 7 = 72 - 7 = 67°
⇒ Their angles are equal (in ΔLMN and ΔSTU)
⇒ ΔLMN and ΔSTU are similar
