Question

Find the value of x. Then select the correct set of angle measures for this triangle.

Answer 1

B. 31°, 106°, and 43°

Step-by-step explanation

First, we have to find the value of x. Knowing that the sum of the measures of all the interior angles of a triangle is 180°, we can write an equation for x,

`(5x-7)+(11x-4)+(3x+1)=180`

Add like terms,

`\begin{gathered} (5x+11x+3x)+(-7-4+1)=180 \\ \\ 19x-10=180 \end{gathered}`

Add 10 to both sides,

`\begin{gathered} 19x-10+10=180+10 \\ \\ 19x=190 \end{gathered}`

And divide both sides by 19,1

`\begin{gathered} (19x)/(19)=(190)/(19) \\ \\ x=10 \end{gathered}`

Now, replace the value of x = 10 in the expressions for each angle's measure to find their values,

`\begin{cases}5x-7=5\cdot10-7=50-7=43 \\ {11x-4=11\cdot10-4=110-4=106} \\ {3x+1=3\cdot10+1=30+1=31}\end{cases}`

Hence, the set of angle measures for this triangle is 31°, 106°, and 43°.