Question

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.

Answer 1

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

$(120\°+y)+y+3y=180\°$

$5y+120\°=180\°$

$5y=180\°-120\°$

$y=60\°/5=12\°$

Find the measure of x

$x=120\°+12\°=132\°$

Find the measure of z

$z=3(12\°)=36\°$

therefore

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