Find the measure of each angle in this triangle.

Question

The measure of the largest angle of a triangle is 10 degrees less than the sum of the other two and the second is twice the measure of the smallest angle.

Answer 1

First note that the 3 angles of a triangle add to 180 degrees

If L = measure of largest angle

   M = measure of middle sized angle

   S = measure of smallest angle

 

1)  L + S + M = 180

 

2)  L = S + M - 10

 

3)  M = 2S

 

This is the information we know from the problem.

 

Replace M with 2S in equation 2

 

L = S + 2S - 10

L = 3S - 10

 

Put this information into the first equation

L + S + M = 180

(3S-10) + S + 2S = 180   combine like terms

6S - 10 = 180                  add 10 to both sides

6S = 190                         divide both sides by 6

S = 190/6

S = 31 2/3 degrees

 

M = 2S = 2(190/6) = 190/3 + 63 1/3 degrees

 

L = 3S - 10

  = 3(190/6) + 10

  = 190/2 + 10

  = 95 + 10

L = 105 degrees

 

Your angles are:

smallest = 31 2/3 degrees

mid size = 63 1/3 degrees

largest = 105 degrees