Question

I need to solve question E using factoring and showing work, i have no idea how

Answer 1

As shown in the graph above, the point G is in the interior of the right angled triangle. Angle ABG measures (x^2 + 3x) while angle CBG measures 40x.

Angles ABG and CBG add up to 90 and that gives you;

`\begin{gathered} x^2+3x+40=90 \\ x^2+43x-90=0 \\ \text{Factorize and you have} \\ (x+45)(x-2)=0 \\ \text{This means } \\ x+45=0 \\ x=-45 \\ OR \\ x-2=0 \\ x=2 \end{gathered}`

Knowing that we are dealing with a positive angle measure, we shall take x = 2 (and not x = -45)

Therefore, x = 2, and angle ABG measures

`\begin{gathered} x^2+3x \\ 2^2+3(2) \\ 4+6 \\ 10 \end{gathered}`

Also angle CBG measures;

`\begin{gathered} 40x \\ 40(2) \\ 80 \end{gathered}`