Question

1) Determine os valores desconhecidos apresentados nos polígonos a seguir, de acordo

com o exemplo da letra a e b.


2) Calcule o valor desconhecido dos ângulos em graus.

Answer 1

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Soma dos ângulos internos de um triângulo qualquer

$\boxed{\begin{array}{c}\sf a+b+c=180^\circ\\\sf a,b~e~c~s\tilde ao~\hat angulos~quaisquer~de~tri\hat angulo. \end{array}}$

1)

$\tt c)~\sf x=180^\circ-80^\circ\\\boxed{\sf x=100^\circ}\\\sf y=180^\circ-130^\circ\\\boxed{\sf y=50^\circ}$

$\tt e)~\sf x=180^\circ-110^\circ\\\boxed{ x=70^\circ}\\\sf y=180^\circ-95^\circ\\\boxed{\sf y=85^\circ}$

$\tt f)~\sf x=180^\circ-30^\circ\\\boxed{\sf x=150^\circ}\\\sf y=180^\circ-60^\circ\\\boxed{\sf y=120^\circ}\\\sf z=180^\circ-90^\circ\\\boxed{\sf z=90^\circ}$

$\tt g)~\sf x=180^\circ-75^\circ\\\boxed{\sf x=105^\circ}\\\sf y=180^\circ-120^\circ\\\boxed{\sf y=60^\circ}$

2)

$\tt a)~\sf2x+3x+x=180^\circ\\\sf6x=180^\circ\\\sf x=\dfrac{180^\circ}{6}\\\boxed{\sf x=30^\circ}\\\tt b)~\sf70^\circ+40^\circ+x=180^\circ\\\sf x+110^\circ=180^\circ\\\sf x=180^\circ-110^\circ\\\boxed{\sf x=70^\circ}\\\tt c)~x+80^\circ+40^\circ=180^\circ\\\sf x+120^\circ=180^\circ\\\sf x=180^\circ-120^\circ\\\boxed{\sf x=60^\circ}\\\tt d)~\sf 2x+3x+4x=180^\circ\\\sf 9x=180^\circ\\\sf x=\dfrac{180^\circ}{9}\\\boxed{\sf x=20^\circ}\\\tt e)~\sf 2x+20^\circ+4x+40^\circ+6x+60^\circ=180^\circ\\\sf12x+120^\circ=180^\circ\\\sf 12x=180^\circ-120^\circ\\\sf12x=60^\circ\\\sf x=\dfrac{60^\circ}{12}\\\boxed{\sf x=5^\circ}$

$\tt f)~\sf 2x+8x+4^\circ+x=180^\circ\\\sf11x=180^\circ-4^\circ\\\sf 11x=176^\circ\\\sf x=\dfrac{176^\circ}{11}\\\boxed{\sf x=16^\circ}\\\tt g)~\sf2x+3x+x=180^\circ\\\sf6x=180^\circ\\\sf x=\dfrac{180^\circ}{6}\\\boxed{\sf x=30^\circ}\\\tt h)~\sf x+x+50^\circ+10^\circ\\\sf2x+60^\circ=180^\circ\\\sf 2x=180^\circ-60^\circ\\\sf 2x=120^\circ\\\sf x=\dfrac{120^\circ}{2}\\\boxed{\sf x=60^\circ}$