Answer: ∠A = 20°; ∠B = 59°; ∠C = 101°
Step-by-step explanation:
According to the problem:
- ∠A = ∠A
- ∠B = 4 · ∠A - 21°
- ∠C = 5 · ∠A + 1°
All interior angles within a triangle adds up to 180°:
∠A + ∠B + ∠C = 180°
[tex]A+(4A-21)+(5A+1)=180\\\\A+4A+5A-21+1=180\\\\10A=180+21-1\\\\10A=200\\\\A=20\°[/tex]
Substitute in the value of ∠A into the other equations:
∠B = 4 · ∠A - 21° = 4(20°) - 21° = 80° - 21° = 59°
∠C = 5 · ∠A + 1° = 5(20°) + 1° = 100° + 1° = 101°
