Question

In the figure, GK bisects FGH

if FGK=7w+3 and FGH=104, find W.

7
3.5
14.43
52

PLEASE HELP ME!!!!

Answer 1

The value of w in the diagram is 7. ( option A)

Since GK is the bisector of angle FGH, this. means that

angle FGK is equal to angle GHK

therefore we can say that

angle FGH = 2 ( FGK)

angle FGK = 7w + 3

and FGH = 104

Therefore;

2( 7w + 3 ) = 104

= 14w + 6 = 104

collect like terms

14w = 104 - 6

14w = 98

divide both sides by 14

w = 98/14

w = 7

Therefore, the value of w in the diagram is 7

Answer 2

`w = 7`

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

`(104)/(2) = (2*(7w + 3))/(2)`

`52 = 7w + 3`

Subtract 3 from each side

`52 - 3 = 7w + 3 - 3`

`49 = 7w`

Divide both sides by 7

`(49)/(7) = (7w)/(7)`

`7 = w`

`w = 7`