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ki77a [65]
3 years ago
14

Em um triangulo ABC,a medida do angulo BAC excede a medida de ABC em 10°,e a medida do amgulo ACB,adicionada de 30°,é igual ao d

obro da medida de BAC.Quais são as medidas dos angulos deste triangulo?
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
4 0
the question in English is

<span>In a triangle ABC, the measure of the BAC angle exceeds the ABC measure by 10 °, and the measure of the ACB angle, added by 30 °, is equal to twice the BAC measure. What are the measures of the angles of this triangle?
</span>
Let 
A=m ∠BAC
B=m∠ABC
C=m∠ACB

we know that
A+B+C=180-----> equation 1
A=B+10-----> B=A-10------> equation 2
C+30=2A----> C=2A-30----> equation 3

substitute equation 2 and equation 3 in equation 1
A+[A-10]+2A-30]=180------> 4A=180+40-----> A=220/4-----> A=55°
B=A-10----> B=55-10-----> B=45°
C=2A-30-----> C=2*55-30----> C=80°

the answer is
m ∠BAC is 55°
m∠ABC is 45°
m∠ACB is 80°

<span>the answer in Portuguese

</span><span>Deixei
</span>A=m ∠BAC
B=m∠ABC
C=m∠ACB

<span>nós sabemos isso
</span>A+B+C=180-----> <span>equação 1
</span>A=B+10-----> B=A-10------> equação 2
C+30=2A----> C=2A-30----> equação 3

substitute equação 2 e equação 3 dentro equação 1
A+[A-10]+2A-30]=180------> 4A=180+40-----> A=220/4-----> A=55°
B=A-10----> B=55-10-----> B=45°
C=2A-30-----> C=2*55-30----> C=80°

<span>a resposta é
</span>m ∠BAC is 55°
m∠ABC is 45°
m∠ACB is 80°

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