Question

am nevoie repedeeee acummm!!!

Answer 1

Notam unghiurile cu a,b,c,d

Suma unghiurilor unui patrulater este egala cu 360°

a+b+c+d=360

a)

a=b

c=2d

d=a+5

Inlocuim si obtinem:

b=a

c=2(a+5)

d=a+5

a+a+2a+10+a+5=360

5a=345

a=69°

d=74°

b=69°

c=148°

b)

$\frac{a}{3} =\frac{b}{3} =\frac{c}{4} =\frac{d}{5} =k$

a=3k

b=3k

c=4k

d=5k

3k+3k+4k+5k=360

15k=360

k=24

a=72°

b=72°

c=96°

d=120°

c)

d=110°

c=3b

a:b=2 rest 10

Aplicam teorema impartirii cu rest: deimpartitul este egal cu suma dintre rest si produsul dintre cat si impartitor

a=2b+10

a+b+c+d=360

2b+10+b+3b+110=360

6b=240

b=40°

a=90°

c=120°

d)

$\frac{a}{4} =\frac{b}{3} =\frac{c}{2} =k\\\\a=4k\\\\b=3k\\\\c=2k\\\\\frac{c}{\frac{1}{6} } =\frac{d}{\frac{1}{4} } =n\\\\c=\frac{n}{6} \\\\d=\frac{n}{4} \\\\2k=\frac{n}{6} \\\\n=12k$

d=3k

a=4k

b=3k

c=2k

4k+3k+2k+3k=360

12k=360

k=30°

a=120°

b=90°

c=60°

d=90°

e)

a+b+c=330°

b+c=2a

Inlocuim in prima relatie:

a+2a=330

a=110°

b+c=220°

b=40+c

Inlocuim in prima relatie:

40+c+c=220

2c=180

c=90°

b=130°

d=360-(110+130+90)=30°

f)

$\frac{a}{\frac{1}{0,5} } =\frac{b}{\frac{1}{0,2} } =\frac{c}{\frac{1}{0,(3)} } =\frac{d}{\frac{1}{0,8} } =k$

a=2k

b=5k

c=3k

d=1,25k

2k+5k+3k+1,25k=360

11,25k=360

k=32

a=64°

b=160°

c=96°

d=40°

Un alt exercitiu gasesti aici: brainly.ro/tema/142410

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