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!
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