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in triangle abc, if m∠a is six less than 7 times x, m∠b is five less than three times x, and m∠c is five less than four times x, find x and the measure of each angle.

Respuesta :

calculista

Answer:

m∠a=92°

m∠b=37°

m∠c=51°

Step-by-step explanation:

we know that

The sum of the measure of the internal angles of a triangle must be equal to 180 degrees

we have that

m∠a+m∠b+m∠c=180°  -----> equation A

m∠a=(7x-6)°

m∠b=(3x-5)°

m∠c=(4x-5)°

substitute the given values in the equation A and solve for x

[tex](7x-6)\°+(3x-5)\°+(4x-5)\°=180\°[/tex]

[tex](14x-16)=180[/tex]

[tex]14x=196[/tex]

[tex]x=14[/tex]

Find the measure of each angle

m∠a=(7(14)-6)=92°

m∠b=(3(14)-5)=37°

m∠c=(4(14)-5)=51°

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