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The angles in a triangle are such that one angle is 120 degrees more than the smallest angle, while the third angle is 3 times as large as the smallest angle. Find the measures of all three angles.

Respuesta :

calculista

Answer:

The measures of the angles are

[tex]132\°[/tex], [tex]12\°[/tex] and [tex]36\°[/tex]

Step-by-step explanation:

Let

x-----> one angle

y----> the smallest angle

z----> the third angle

we know that

[tex]x+y+z=180\°[/tex] -----> equation A

[tex]x=120\°+y[/tex] ----> equation B

[tex]z=3y[/tex] -----> equation C

substitute equation B and equation C in equation A and solve for y

[tex](120\°+y)+y+3y=180\°[/tex]

[tex]5y+120\°=180\°[/tex]

[tex]5y=180\°-120\°[/tex]

[tex]y=60\°/5=12\°[/tex]

Find the measure of x

[tex]x=120\°+12\°=132\°[/tex]

Find the measure of z

[tex]z=3(12\°)=36\°[/tex]

therefore

The measures of the angles are [tex]132\°[/tex], [tex]12\°[/tex] and [tex]36\°[/tex]

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