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

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) (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) (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

RELATED QUESTIONS
The angles of a triangle add up to 180 degrees. The second angle is 30 degrees larger... (answered by mamiya)
The angles of a triangle add up to 180 degrees. The second angle is 25 degrees larger... (answered by josgarithmetic)
Three angles in a triangle add up to 180 degrees. The largest angle is two degrees more... (answered by MathLover1,MathTherapy)
Alejandra knows the angles in a triangle add up to 180 degrees. The measure of the first... (answered by ikleyn)
The three angles in a triangle always add up to 180 degrees. In a triangle,one angle... (answered by AnlytcPhil)
the smallest angle in a triangle is one-third of the largest angle.The third angle is 20... (answered by solver91311)
The sum of the angles of a triangle is 180 degrees. If one angle of a triangle is ten... (answered by stanbon)
How do I solve the following: The three angles in a triangle always add up to 180... (answered by stanbon,ewatrrr)
The sum of the angles of a triangle is 180. Find teh three angles of the triangle if one... (answered by orca)