Question

The second angle of a triangle measures three times as large as the first. If the third angle measures 55 degrees more than the first, find the measure of all three angles. ( recall that the sum of the angles of a triangle add to 180 degrees )

Answer 1

Taking x as the measure of the first triangle, we know that the second one measures three times as x:

`3x`

And the third one measures 55 degrees more than the first:

`x+55`

We know that the sum of the angles of a triangle is 180, use this information to find x:

`\begin{gathered} x+3x+(x+55)=180 \\ 5x+55=180 \\ 5x=180-55 \\ x=(125)/(5) \\ x=25 \end{gathered}`

It means that the first angle measures 25°. Use this value to find the second and third angles:

`\begin{gathered} 3x=3\cdot25=75 \\ x+55=25+55=80 \end{gathered}`

It means that the second angle measures 75° and the third one measures 80°.