Question

In the figure, GK bisects FGH

Answer 1

Answer:

$w = 7$

Step-by-step explanation:

Given:

m<FGK = (7w + 3)°

m<FGH = 104°

angle bisector of <FGH = GK

Required:

Value of w

SOLUTION:

Since GK bisects angle FGH, it divides the angle into two equal parts. Therefore, the following equation can be generated to find the value of w:

m<FGH = 2*m<FGK

$104 = 2*(7w + 3)$ (substitution)

Divide both sides by 2

$\frac{104}{2} = \frac{2*(7w + 3)}{2}$

$52 = 7w + 3$

Subtract 3 from each side

$52 - 3 = 7w + 3 - 3$

$49 = 7w$

Divide both sides by 7

$\frac{49}{7} = \frac{7w}{7}$

$7 = w$

$w = 7$