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

Find the value of x. Then select the correct set of angle measures for this triangle-example-1
User Grault
by
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1 Answer

6 votes

ANSWER

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°.

User Dafang Cao
by
7.7k points