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.
1 answer:
Answer:
The measures of the angles are
,
and ![36\°](https://tex.z-dn.net/?f=36%5C%C2%B0)
Step-by-step explanation:
Let
x-----> one angle
y----> the smallest angle
z----> the third angle
we know that
-----> equation A
----> equation B
-----> equation C
substitute equation B and equation C in equation A and solve for y
<em>Find the measure of x</em>
![x=120\°+12\°=132\°](https://tex.z-dn.net/?f=x%3D120%5C%C2%B0%2B12%5C%C2%B0%3D132%5C%C2%B0)
<em>Find the measure of z</em>
![z=3(12\°)=36\°](https://tex.z-dn.net/?f=z%3D3%2812%5C%C2%B0%29%3D36%5C%C2%B0)
therefore
The measures of the angles are
,
and ![36\°](https://tex.z-dn.net/?f=36%5C%C2%B0)
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