Atividade: Soma dos Ângulos Internos de Quadriláteros

Nesta atividade, nós vamos praticar a calcular a amplitude do ângulo em falta num quadrilátero sabendo que a soma dos ângulos num quadrilátero é 360 graus.

Q1:

๐ด ๐ต ๐ถ ๐ท รฉ um quadrilรกtero onde ๐‘š ( ๏‚— ๐ด ) = 1 6 5 โˆ˜ , ๐‘š ( ๐ด ๏‚— ๐ต ๐ถ ) = 4 ๐‘ฅ โˆ˜ , ๐‘š ( ๐ต ๏‚— ๐ถ ๐ท ) = 4 ๐‘ฅ โˆ˜ , e ๐‘š ( ๐ถ ๏‚— ๐ท ๐ด ) = 5 ๐‘ฅ โˆ˜ . Qual รฉ o valor de ๐‘ฅ ?

Q2:

Na figura apresentada, ฬ‚ ๐ด = 7 4 โˆ˜ e ฬ‚ ๐ถ = 9 2 โˆ˜ . Determina ฬ‚ ๐ท .

Q3:

Determine o valor de ๐‘ฅ no quadrilรกtero dado.

Q4:

Determina ฬ‚ ๐ด .

Q5:

Em um quadrilรกtero ๐ด ๐ต ๐ถ ๐ท , se ๐‘š ( ๏‚— ๐ด ) = 3 ๐‘š ( ๏‚— ๐ต ) = 3 ๐‘š ( ๏‚— ๐ถ ) = 7 2 โˆ˜ , encontre ๐‘š ( ๏‚— ๐ท ) .

Q6:

A soma das medidas dos รขngulos de um trapรฉzio รฉ 3 6 0 โˆ˜ . Escreva uma equaรงรฃo para encontrar a medida que falta ๐‘ฅ , e resolva-o.

  • A ๐‘ฅ + 1 0 2 = 1 8 0 , ๐‘ฅ = 7 8
  • B ๐‘ฅ + 1 0 2 + 1 1 6 = 3 6 0 , ๐‘ฅ = 1 0 2
  • C ๐‘ฅ + 1 0 2 + 1 1 6 + 7 8 = 3 6 0 , ๐‘ฅ = 7 8
  • D ๐‘ฅ + 1 0 2 + 1 1 6 + 7 8 = 3 6 0 , ๐‘ฅ = 6 4
  • E ๐‘ฅ + 1 0 2 = 1 8 0 , ๐‘ฅ = 1 0 2

Q7:

Para a figura dada, na qual ๐ถ ฬ‚ ๐ท ๐ด = 5 ๐‘ฅ โˆ˜ , ๐ต ฬ‚ ๐ถ ๐ท = 7 ๐‘ฆ โˆ˜ e ๐ด ฬ‚ ๐ต ๐ถ = 8 ๐‘ฆ โˆ˜ , determina os valores de ๐‘ฅ e ๐‘ฆ .

  • A ๐‘ฅ = 9 5 , ๐‘ฆ = 8 4
  • B ๐‘ฅ = 9 5 , ๐‘ฆ = 1 2
  • C ๐‘ฅ = 1 9 , ๐‘ฆ = 9 5
  • D ๐‘ฅ = 1 9 , ๐‘ฆ = 1 2

Q8:

Dado que ๐‘š ( ๏‚— ๐ท ) = 2 3 ๐‘š ( ๏‚— ๐ต ) , encontre ๐‘š ( ๏‚— ๐ต ) e ๐‘š ( ๏‚— ๐ท ) .

  • A ๐‘š ( ๏‚— ๐ต ) = 5 3 โˆ˜ , ๐‘š ( ๏‚— ๐ท ) = 1 2 7 โˆ˜
  • B ๐‘š ( ๏‚— ๐ต ) = 7 2 โˆ˜ , ๐‘š ( ๏‚— ๐ท ) = 1 0 8 โˆ˜
  • C ๐‘š ( ๏‚— ๐ต ) = 1 2 7 โˆ˜ , ๐‘š ( ๏‚— ๐ท ) = 5 3 โˆ˜
  • D ๐‘š ( ๏‚— ๐ต ) = 1 0 8 โˆ˜ , ๐‘š ( ๏‚— ๐ท ) = 7 2 โˆ˜

Q9:

Determine ๐‘š ( ๐ถ ๏‚— ๐ด ๐ต ) .

Q10:

A partir da figura, determine ๐‘š ( ๐ต ๏‚— ๐ธ ๐ท ) .

  • A 3 2 โˆ˜
  • B 8 0 โˆ˜
  • C 2 2 โˆ˜
  • D 4 2 โˆ˜
  • E 9 0 โˆ˜

Q11:

Na figura, ๐‘š ( ๏‚— ๐ด ) = 3 4 โˆ˜ , ๐‘š ( ๏‚— ๐น ) = 4 8 โˆ˜ , e ๐‘š ( ๐ต ๏‚— ๐ธ ๐น ) = 3 4 โˆ˜ . Determine a medida de todos os รขngulos em ๐ท ๐ธ ๐ต ๐ถ .

  • A ๐‘š ( ๐ธ ๏‚— ๐ต ๐ถ ) = 4 8 โˆ˜ , ๐‘š ( ๏‚— ๐ถ ) = 6 4 โˆ˜ , ๐‘š ( ๐ต ๏‚— ๐ธ ๐ท ) = 3 4 โˆ˜ , ๐‘š ( ๐ธ ๏‚— ๐ท ๐ถ ) = 2 1 4 โˆ˜
  • B ๐‘š ( ๐ธ ๏‚— ๐ต ๐ถ ) = 8 2 โˆ˜ , ๐‘š ( ๏‚— ๐ถ ) = 9 8 โˆ˜ , ๐‘š ( ๐ต ๏‚— ๐ธ ๐ท ) = 3 4 โˆ˜ , ๐‘š ( ๐ธ ๏‚— ๐ท ๐ถ ) = 1 4 6 โˆ˜
  • C ๐‘š ( ๐ธ ๏‚— ๐ต ๐ถ ) = 6 4 โˆ˜ , ๐‘š ( ๏‚— ๐ถ ) = 8 2 โˆ˜ , ๐‘š ( ๐ต ๏‚— ๐ธ ๐ท ) = 1 1 6 โˆ˜ , ๐‘š ( ๐ธ ๏‚— ๐ท ๐ถ ) = 9 8 โˆ˜
  • D ๐‘š ( ๐ธ ๏‚— ๐ต ๐ถ ) = 8 2 โˆ˜ , ๐‘š ( ๏‚— ๐ถ ) = 6 4 โˆ˜ , ๐‘š ( ๐ต ๏‚— ๐ธ ๐ท ) = 1 4 6 โˆ˜ , ๐‘š ( ๐ธ ๏‚— ๐ท ๐ถ ) = 6 8 โˆ˜

Q12:

Determine ๐‘š ( ๐น ๏‚— ๐ธ ๐ถ ) .

Q13:

Na figura, se ฬ‚ ๐ด = 2 6 โˆ˜ , ๐ด ฬ‚ ๐ถ ๐ต = 5 4 โˆ˜ , ฬ‚ ๐น = 1 4 6 โˆ˜ , determina ฬ‚ ๐ธ .

Q14:

Os รขngulos internos de um quadrilรกtero tรชm razรฃo 3 โˆถ 4 โˆถ 5 โˆถ 6 . Qual รฉ o maior รขngulo?

  • A 6 0 โˆ˜
  • B 2 0 โˆ˜
  • C 8 0 โˆ˜
  • D 1 2 0 โˆ˜

Q15:

Na figura dada, encontre ๐‘ฅ e ๐‘ฆ .

  • A ๐‘ฅ = 1 9 , ๐‘ฆ = 4 8
  • B ๐‘ฅ = 9 6 , ๐‘ฆ = 1 1 8
  • C ๐‘ฅ = 1 6 , ๐‘ฆ = 5 9
  • D ๐‘ฅ = 1 6 , ๐‘ฆ = 3 1
  • E ๐‘ฅ = 1 4 , ๐‘ฆ = 3 1

Q16:

Encontre as medidas dos รขngulos de um quadrilรกtero, dado que a relaรงรฃo entre eles รฉ 6 9 1 2 1 3 : : : .

  • A 6 3 โˆ˜ , 1 1 7 โˆ˜ , 5 4 โˆ˜ , 1 2 6 โˆ˜
  • B 1 5 โˆ˜ , 1 8 โˆ˜ , 2 1 โˆ˜ , 2 2 โˆ˜
  • C 8 7 โˆ˜ , 8 1 โˆ˜ , 9 3 โˆ˜ , 9 9 โˆ˜
  • D 5 4 โˆ˜ , 8 1 โˆ˜ , 1 0 8 โˆ˜ , 1 1 7 โˆ˜
  • E 2 2 โˆ˜ , 2 8 โˆ˜ , 3 7 โˆ˜ , 4 9 โˆ˜

Q17:

๐ด ๐ต ๐ถ ๐ท รฉ um quadrilรกtero onde ๐‘š ( ๏‚— ๐ด ) = 1 6 2 โˆ˜ , ๐‘š ( ๐ด ๏‚— ๐ต ๐ถ ) = 4 ๐‘ฅ โˆ˜ , ๐‘š ( ๐ต ๏‚— ๐ถ ๐ท ) = 2 ๐‘ฅ โˆ˜ , e ๐‘š ( ๐ถ ๏‚— ๐ท ๐ด ) = 3 ๐‘ฅ โˆ˜ . Qual รฉ o valor de ๐‘ฅ ?

Q18:

Determina ฬ‚ ๐ด .

Q19:

Determina ฬ‚ ๐ด .

Q20:

Determine o valor de ๐‘ฅ no quadrilรกtero dado.

Q21:

Determine o valor de ๐‘ฅ no quadrilรกtero dado.

Q22:

Em um quadrilรกtero ๐ด ๐ต ๐ถ ๐ท , se ๐‘š ( ๏‚— ๐ด ) = 9 ๐‘š ( ๏‚— ๐ต ) = 5 ๐‘š ( ๏‚— ๐ถ ) = 4 5 โˆ˜ , encontre ๐‘š ( ๏‚— ๐ท ) .

Q23:

Na figura apresentada, ฬ‚ ๐ด = 6 0 โˆ˜ e ฬ‚ ๐ถ = 1 1 8 โˆ˜ . Determina ฬ‚ ๐ท .

Q24:

Na figura apresentada, ฬ‚ ๐ด = 7 5 โˆ˜ e ฬ‚ ๐ถ = 9 6 โˆ˜ . Determina ฬ‚ ๐ท .

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