Question

If mZFGK = 4y - 4 and m ZKGH = 3y + 2, find x.A. 24C. 20B. 40D. 6

Answer 1

GK bisects the angle FGH

So, angle FGK= angle HGK

It is given that :

`\begin{gathered} \angle FGK=x\text{ \& }\angle HGK=y \\ \text{thus, x = y} \end{gathered}`

Since,

`\begin{gathered} \angle FGK=4v-4\text{ \& }\angle KGH=3v+2 \\ As\text{ : }\angle FGK=\angle KGH \\ 4v-4=3v+2 \end{gathered}`

Simplify the expression:

`\begin{gathered} 4v-4=3v+2 \\ 4v-3v=4+2 \\ v=6 \\ \text{Thus, m}\angle FGK=4v-4 \\ \text{Substitute the value of v =6} \\ m\angle FGK=4(6)-4 \\ m\angle FGK=24-4 \\ m\angle FGK=20 \end{gathered}`

Since, from the figure:

`\begin{gathered} m\angle FGK=x \\ \text{thus, x = 20} \end{gathered}`

Answer: C) 20