Respuesta :
Given the triangle QRS, you know it is isosceles with base QR, and:
[tex]\begin{gathered} m\angle Q=\mleft(3x+41\mright)\text{\degree} \\ m\angle R=\mleft(5x+27\mright)\text{\degree} \end{gathered}[/tex]By definition, an Isosceles Triangle is a triangle that has two equal sides and two equal angles. Therefore, you can determine that, in this case:
[tex]m\angle Q=m\angle R[/tex]Then, you can set up the following equation with the expressions that represent each angle:
[tex]3x+41=5x+27[/tex]Solve for "x" in order to find its value:
[tex]\begin{gathered} 3x-5x=27-41 \\ \\ -2x=-14 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-14}{-2} \\ \\ x=7 \end{gathered}[/tex]Knowing the value of "x", you can determine that:
[tex]m\angle Q=m\angle R=(3(7)+41)\text{\degree}=(21+41)\text{\degree}=62\text{\degree}[/tex]By definition, the sum of the interior angles of a triangle is 180 degrees. Therefore, you can set up this equation:
[tex]m\angle S+62\text{\degree}+62\text{\degree}=180\text{\degree}[/tex]Solving for angle S, you get:
[tex]\begin{gathered} m\angle S=180\text{\degree}-124\text{\degree} \\ m\angle S=180\text{\degree}-124\text{\degree} \\ m\angle S=56\text{\degree} \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} m\angle Q=62\text{\degree} \\ m\angle R=62\text{\degree} \\ m\angle S=56\text{\degree} \end{gathered}[/tex]