Question

he sum of the measure of the angles in triangle ABC is 180o. The sum of the measures of angle B and angle C is twice the measure of angle A. The measure of angle B is 32o less than the measure of angle C.Create a system of equations and solve using matrices to find the measure of each of the three angles.

Answer 1

• A = 60°
• B = 44°
• C = 76°

Explanation:

The given relations can be expressed using the equations ...

A +B +C = 180

2A -B -C = 0

B -C = -32

The augmented matrix representing these equations is ...

`\left[\begin{array}c1&1&1&180\\2&-1&-1&0\\0&1&-1&-32\end{array}\right]`

Its solution is easily found using a suitable calculator:

(A, B, C) = (60, 44, 76)

The measures of the angles are ...

• A = 60°
• B = 44°
• C = 76°

_____

Additional comment

Adding the first two rows gives 3A=180, or A=60. Now you know the sum of B and C is 120, and their difference is 32. Adding and subtracting these equations get you to B = (120 -32)/2 = 44, and C = (120 +32)/2 = 76. Setting up and solving the matrix equation version takes a little longer.