SOLUTION: the second angle of a triangle is 3 times as large as the first. the third angle is 75 degrees more than the first. find the measure of the smallest angle. A)105 B)15 C)21 D)7

Question 223947: the second angle of a triangle is 3 times as large as the first. the third angle is 75 degrees more than the first. find the measure of the smallest angle.
A)105
B)15
C)21
D)75
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = "the first angle
:
Write an equation for each statement
:
"the second angle of a triangle is 3 times as large as the first"
3x = the second angle
:
"the third angle is 75 degrees more than the first."
x + 75 = the third angle
:
find the measure of the smallest angle.
we know the 3 angle add up to 180, therefore
:
x + 3x + (x+75) = 180
:
x + 3x + x + 75 = 180
:
subtract 75 from both sides, add up the x's
5x = 180 - 75
:
5x = 105
:
divide both sides by 5
x =
x = 21
:
You should be able to find the other two angles, make sure all 3 add up to 180
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