Question 595896: The angles of a triangle add up to 180 degrees.
The second angle is 30 degrees larger than the smallest angle.
The third angle is 4 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees)
Answer by mamiya(56)   (Show Source):
You can put this solution on YOUR website! let x be the angle of the smallest one, y the second angle and z the third one.
we know that the angles of a triangle add up to 180 degrees, so x+y+z = 180
The second angle is 30 degrees larger than the smallest angle, y = x + 30
The third angle is 4 times as big as the smallest angle, z = 4x
x+y+z= 180
so we get this system of equations y= x +30
z = 4x
by plugging the last two equations into the first one , we get
x+y+z=180 --> x + x+30 + 4x = 180
--> 6x + 30 = 180
--> 6x = 180-30
--> 6x = 150
--> x = 150/6
--> x = 25
so the measure of the smallest angle is 25 degrees.
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