Question

The sum of the measures of the angles of a triangle sum to 180 degrees. The sum of the measures of the second and third angles is 3 times the measure of the first angle. The third angle is 13.2 more than the second angle. Find the measure of the third angle.

Answer 1

Systems of Equations

When solving systems of equations, we must first assign variables to given subjects, and reword the problem into equations.

Solving the Question

Let the angles be x, y and z.

We're given:

• Sum of angles = 180
  ⇒ Rearrange into equation:
  ⇒
  `x+y+z=180`
• Second angle + third angle = 3 times first angle
  ⇒ Rearrange into equation:
  ⇒
  `y+z=3x`
• Third angle = 13.2 more than second angle
  ⇒ Rearrange into equation:
  ⇒
  `z = 13.2+y`

Combine the first and second equations using substitution:

`x+y+z=180\\x+3x=180\\4x=180\\x=45`

Therefore, the first angle measures 45 degrees.

Plug this answer into
`x+2y=166.8` and solve for y:

`x+2y=166.8\\45+2y=166.8\\2y=121.8\\y=60.9`

Therefore, the second angle measures 60.9 degrees.

Finally, subtract these answers from 180 to find the third angle:

`180-60.9-45\\=74.1`

Therefore, the third angle measures 74.1 degrees.

Answer

First angle: 45 degrees

Second angle: 60.9 degrees

Third angle: 74.1 degrees