SOLUTION: the meassure of one triangel is 28 more than the measure of the smallest angel of the triangle. the measure of the 3rd angel is twice the measure of the smallest angel. find all 3

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Question 103734This question is from textbook Geometry
: the meassure of one triangel is 28 more than the measure of the smallest angel of the triangle. the measure of the 3rd angel is twice the measure of the smallest angel. find all 3 measures. This question is from textbook Geometry

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
First, you know (or should know) that the sum of the angels-oops!... angles in any plane triangle is equal to 180 degrees. So, if the three angles are labeled A, B, and C, you can write:
1) A+B+C = 180 and, from the problem description, you can write:
2) A = B+28 "The measure of one angle is 28 degrees more than the smallest angle"
3) C = 2B "The third angle is twice the measure of the smalles angle"
Now, substitute the A and C from equations 2) and 3) into equation 1) and solve for B.
1a) (B+28)+B+2B = 180 Simplify and solve for B
4B+28 = 180 Subtract 28 from both sides.
4B = 152 Divide both sides by 4.
B = 38
A = B+28
A = 38+28
A = 66
C = 2B
C = 2(38)
C = 76
The three angles are:
A = 66 degrees.
B = 38 degrees.
C = 76 degrees.
Check:
A+B+C = 180
66+38+76 = 180 OK!
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