Question

The angle measures in a triangle are (3x+4), (5x), and (7x-4). What is the measure of the largest angle in the triangle?12 degrees40 degrees60 degrees80 degrees

Answer 1

80 degrees

Step-by-step explanation:

The sum of the measures of angles in a triangle is 18 degrees.

Given that the angle measures in a triangle are (3x+4), (5x), and (7x-4), then:

`(3x+4)+(5x)+(7x-4)=180^0`

First, we solve the equation for x.

`\begin{gathered} 3x+5x+7x+4-4=180^0 \\ 15x=180^0 \\ x=(180^0)/(15) \\ x=12^0 \end{gathered}`

Therefore, the measures of the angles are:

`\begin{gathered} 3x+4=3(12)+4=40^0 \\ 5x=5(12)=60^0 \\ 7x-4=7(12)-4=80^0 \end{gathered}`

The measure of the largest angle in the triangle is 80 degrees.