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.
:
Three angles, A, B, C. Write an equation for each statement
:
 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
:
"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