Question

9,10,11 va roooggg dau coroana!!!!

Answer 1

Răspuns:

Explicație pas cu pas:

9. ΔDEF

a) ∡D=3·∡E; ∡F=2·∡D=2·3·∡E=6·∡E

∡D+∡E+∡F=180°

3·∡E+∡E+6·∡E=180°  ⇔10·∡E=180°  ⇔∡E=180°/10=18°  

∡E=18°; ∡D=3·18°=54°; ∡F=6·18°=108°

b) ∡F=2·∡D; ∡E=6·∡F=6·2·∡D=12·∡D

∡D+∡E+∡F=180°

∡D+12·∡D+2·∡D=180°  ⇔15·∡D=180°  ⇔∡D=12°

∡E=12·∡D=12·12=144°;  ∡F=2·∡D=2·12°=24°

10. ΔABC

a) ∡B=∡A-17°; ∡C=2·∡A+53°

∡A+∡B+∡C=180°

∡A+∡A-17°+2·∡A+53°=180°  ⇔4·∡A=180°-36°  ⇔4·∡A=144°  ⇔∡A=36°

∡B=∡A-17°=36°-17°=19°; ∡C=2·∡A+53°=2·36°+53°=72°+53°=125°

b) ∡A=2·∡B+3°; ∡C=3·∡B+9°

∡A+∡B+∡C=180°

2·∡B+3°+∡B+3·∡B+9°=180°  ⇔6·∡B+12°=180°  ⇔6·∡B=168°  ⇔∡B=28°

∡A=2·∡B+3°=2·28°+3°=59°; ∡C=3·∡B+9°=3·28°+9°=93°

11. ΔMNP

a) ∡M=∡N; ∡P=(1/2)·∡M

∡M+∡N+∡P=180°

∡M+∡M+(1/2)·∡M=180°  ⇔5·∡M/2=180°  ⇔5·∡M=360°  ⇔∡M=72°

∡N=∡M=72°; ∡P=(1/2)·∡M=(1/2)·72°=36°

b) ∡N=∡P; ∡M=(2/3)·∡P

∡M+∡N+∡P=180°

(2/3)·∡P+∡P+∡P=180° ⇔(2/3)·∡P+2·∡P=180° ⇔8·∡P/3=180° ⇔8·∡P=540°

∡P=540°/8=67,5°; ∡N=∡P=67,5°; ∡M=(2/3)·∡P=(2/3)·67,5°=135°/3=45°