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OverLord2011 [107]
3 years ago
8

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 a

s large as the smallest angle. Find the measures of all three angles.
Mathematics
1 answer:
fomenos3 years ago
3 0

Answer:

The measures of the angles are

132\°, 12\° and 36\°

Step-by-step explanation:

Let

x-----> one angle

y----> the smallest angle

z----> the third angle

we know that

x+y+z=180\° -----> equation A

x=120\°+y ----> equation B

z=3y -----> equation C

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

(120\°+y)+y+3y=180\°

5y+120\°=180\°

5y=180\°-120\°

y=60\°/5=12\°

<em>Find the measure of x</em>

x=120\°+12\°=132\°

<em>Find the measure of z</em>

z=3(12\°)=36\°

therefore

The measures of the angles are 132\°, 12\° and 36\°

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