SOLUTION: One angle of a triangle is twice as large as the smallest angle. The measure of the third angle is 20 more than that of the smallest angle. Find the measure of the smallest angle.

Question 65880: One angle of a triangle is twice as large as the smallest angle. The measure of the third angle is 20 more than that of the smallest angle. Find the measure of the smallest angle.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the angles be: A, B, and C where angle C is the smallest.
From the problem description, we can write:
A = 2C
B = C+20
And, of course, in any plane triangle, the sum of the angles is 180 degrees, so...
A+B+C = 180 Substitute the A and B from above and solve for C, the smallest angle.
2C+C+20+C = 180 Simplify.
4C+20 = 180 Subtract 20 from both sides.
4C = 160 Finally, divide both sides by 4.
C = 40 degrees.
Check:
A+B+C = 2(40)+(40+20)+40 = 80+60+40 = 180 Good!
RELATED QUESTIONS
One angle of a triangle is twice as large as another. The measure of the third angle is... (answered by ankor@dixie-net.com)

One angle of a triangle is twice as large as another. The measure of the third angle is... (answered by stanbon)

Please help me solve: One angle of a triangle is 3 times as large as another. The measure (answered by nerdybill)

One angle of a triangle is three times as large as another. The measure of the third... (answered by mananth,Fombitz)

One angle of a triangle is three times as large as another. The measure of the third... (answered by ikleyn)

ONE ANGLE OF A TRIANGLE IS THREE TIMES AS LARGE AS ANOTHER.THE MEASURE OF THE THIRD ANGLE (answered by waynest)

One angle in a triangle has a measure that is three times as large as the smallest angle. (answered by solver91311)

one angle of a triangle is four times as large as another. The measure of the third... (answered by Boreal)

one angle of a triangle is four times as large as another the measure of the third angle... (answered by dfrazzetto)