Question

Suppose that triangle QRS is isosceles with base QR.Suppose also that angle Q=(3x+41 )degrees and angle R =(5x+27) degrees.Find the degree measure of each angle in the triangle (angles Q, R and S).

Answer 1

Given the triangle QRS, you know it is isosceles with base QR, and:

`\begin{gathered} m\angle Q=\mleft(3x+41\mright)\text{\degree} \\ m\angle R=\mleft(5x+27\mright)\text{\degree} \end{gathered}`

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:

`m\angle Q=m\angle R`

Then, you can set up the following equation with the expressions that represent each angle:

`3x+41=5x+27`

Solve for "x" in order to find its value:

`\begin{gathered} 3x-5x=27-41 \\ \\ -2x=-14 \end{gathered}`
`\begin{gathered} x=(-14)/(-2) \\ \\ x=7 \end{gathered}`

Knowing the value of "x", you can determine that:

`m\angle Q=m\angle R=(3(7)+41)\text{\degree}=(21+41)\text{\degree}=62\text{\degree}`

By definition, the sum of the interior angles of a triangle is 180 degrees. Therefore, you can set up this equation:

`m\angle S+62\text{\degree}+62\text{\degree}=180\text{\degree}`

Solving for angle S, you get:

`\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}`

Hence, the answer is:

`\begin{gathered} m\angle Q=62\text{\degree} \\ m\angle R=62\text{\degree} \\ m\angle S=56\text{\degree} \end{gathered}`