Question

gj bisects ÐFGH, mÐFGJ = (7x - 9)°, and m ÐHGJ = (2x + 36)°. What is m ÐFGH?

Answer 1

GJ bisects FGH, mFGJ = (7x - 9)*, and mHGJ = (2x + 36)*. What is mFGH?

Solution.

Because GJ bisects FGH then

$$\begin{array}{l} \angle FGJ = \angle JGH, \\ 7x - 9 = 2x + 36, \\ 7x - 2x = 36 + 9, \\ 5x = 45, \\ x = 9{}^{\circ}. \end{array}$$

And at last we have

$$\begin{array}{l} \angle FGH = \angle FGJ + \angle JGH, \\ \angle FGH = 7x - 9 + 2x + 36, \\ \angle FGH = 9x + 27, \\ \angle FGH = 9 \cdot 9^{*} + 27, \\ \angle FGH = 108^{*}. \end{array}$$

Answer: $\angle FGH = 108^{*}$