In the triangle PQR we know that its angles have the following measures:
∠P=(6x+5)º
∠Q=(11x-5)º
∠R=xº
To determine the measures of ∠Q, you have to determine the value of x first. To do so you have to keep in mind that the measure of the inner angles of any triangle is 180º, so, for this triangle, the measure of the inner angles can be expressed as:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ (6x+5)+(11x-5)+x=180º \end{gathered}[/tex]From this expression, we can calculate the value of x.
-First, take the parentheses away, order the like terms together and simplify them:
[tex]\begin{gathered} 6x+11x+x+5-5=180º \\ 18x=180º \end{gathered}[/tex]-Second, divide both sides by 18 to determine the value of x:
[tex]\begin{gathered} \frac{18x}{18}=\frac{180}{18} \\ x=10 \end{gathered}[/tex]Now that we know that the value of x is 10º, we can determine the measure of ∠Q by replacing this value on the given expression for its measure:
[tex]\begin{gathered} \angle Q=11x-5 \\ \angle Q=11\cdot10-5 \\ \angle Q=110-5 \\ \angle Q=105º \end{gathered}[/tex]∠Q=105º, the correct option is the third one.