The sum of the angles of a triangle is 180 The largest angle

The sum of the angles of a triangle is 180°. The largest angle is 28° more than the smallest angle. The largest angle is two more degrees than the middle angle. What is the measure of the middle angle? Use an augmented matrix to solve this problem.

Solution

The sum of the angles of a triangle is 180°. The largest angle is 28° more than the smallest angle. The largest angle is two more degrees than the middle angle. What is the measure of the middle angle?

L + M + S = 180 ........................(1)

L = S + 28 .........................(2)

L = M + 2 .......................(3)

Substitute and solve for \"L\'\'

L + (L-2) + (L - 28) = 180

3L -30 = 180

3L = 210

L = 70

Hence, Largest = 70

Plug the value of L into (2) , we get:

70 = M + 2

M = 70 - 2

Hence, Middle = 68 [ Answer ]

Now, plug the value of M into (2) , we get:

70 = S + 28

S = 70 - 28

= 42

Hence, Smallest = 42 [ Answer ]