SOLUTION: In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.

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Question 976589: In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
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Three angles, A, B, C. Write an equation for each statement
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the second angle is twice the measure of the first,
B = 2A
or we divide the equation by 2 and we have this form
A = .5B
and the third angle is three times the measure of the second.
C = 3B
:
We know the sum of the 3 angles has to be 180 degrees
A + B + C = 180
Replace A with .5B and C with 3B
.5A + B + 3B = 180
4.5B = 180
B = 180/4.5
B = 40 degrees
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"Find the measure of the third angle"
We know that C = 3B, therefore
C = 3(40)
C - 120 degrees is the third angle
:
:
We can confirm this by finding the 1st angle and see if the 3 angles add up 180
A = .5(40)
A = 20 degrees
20 + 40 + 120 = 180