Question

Given the triangle is isosceles. If the base angles mZBAC = (7x + 1) and mZBCA = (5x + 9) , what is the measure of the vertex angle?

Answer 1

Given the triangle is isosceles.

Therefore, the base angles would be equal.

`\begin{gathered} 7x+1=5x+9 \\ 7x-5x=9-1 \\ 2x=8 \\ x=(8)/(2)=4 \end{gathered}`

Therefore the base angles are,

`\begin{gathered} 7x+1=7*4+1=29 \\ 5*4+9=20+9=29 \end{gathered}`

As the sum of all the interior angles in triangle is 180, we have,

`\begin{gathered} v\text{ertex angle+}29+29=180 \\ \text{vertex angle=180-29-29=}122 \end{gathered}`

Thus, the vertex angle is 122.