SOLUTION: The angles of a triangle add up to 180 degrees. The second angle is 20 degrees larger than the smallest angle. The third angle is 2 times as big as the smallest angle. Fin

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Question 1202629: The angles of a triangle add up to 180 degrees.
The second angle is 20 degrees larger than the smallest angle.
The third angle is 2 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees).
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

The basic equation is OBVIOUS to anybody, even without explanations

    x + (x+20) + 2x = 180  degrees.


Simplify and find x

    4x + 20 = 180

    4x = 180 - 20

    4x = 160

     x = 160/4 = 40 degrees.


ANSWER.  The smallest angle is 40 degrees.

Solved.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Let a, b, and c represent the angles of the triangle.
We'll have a = smallest angle.

"The angles of a triangle add up to 180 degrees." gives the equation a+b+c = 180.

"The second angle is 20 degrees larger than the smallest angle." gives the equation b = a+20.

"The third angle is 2 times as big as the smallest angle." gives the equation c = 2a

a+b+c = 180
a+(a+20)+c = 180 .... replace b with a+20
a+(a+20)+2a = 180 .... replace c with 2a
4a+20 = 180
4a = 180-20
4a = 160
a = 160/4
a = 40 degrees

The other results b = a+20 and c = 2a will yield larger angles than 40 degrees.
I'll let the student do this part and to verify.

Answer: 40 degrees