gk bisects <fgh
if m<fgk=7w+3 and m<fgh=104, find w
3r+x2=2=4r-2
To find the value of "w," we need to use the angle bisector theorem. According to the angle bisector theorem, if a line segment bisects an angle, it divides the opposite side into two segments proportional to the other two sides.
In this case, "gk" bisects angle <fgh, so we can set up the following proportion:
(GK / GH) = (FK / FH)
We are given that m<fgk = 7w + 3 and m<fgh = 104. Now we can substitute these values into the proportion:
(7w + 3) / GH = FK / FH
Since FK = GK and FH = GH, we can further simplify the equation:
(7w + 3) / GH = GK / GH
Canceling out the GH terms on both sides, we get:
7w + 3 = GK
Now, we need to use the fact that GK is the same as FK because GK bisects the angle. So we rewrite the equation as:
7w + 3 = FK
Finally, we can substitute the given value for m<fgk into the equation:
7w + 3 = 104
Now, we can solve for w:
7w = 104 - 3
7w = 101
w = 101 / 7
w ≈ 14.43
To find the value of w, we need to use the properties of angle bisectors.
From the given information, we know that angle FGK is bisected by GK. This means that the angle measure of FGK is divided into two equal parts, and each part is represented by FGK and BGK.
Let's start by finding the measure of angle BGK. We are given that the measure of angle FGK is equal to 7w + 3. So, we can write FGK = 7w + 3.
Since GK is the angle bisector, we know that the measure of angle BGK is equal to the measure of angle FGH. So, we can write BGK = FGH = 104.
Now we have two equations:
FGK = 7w + 3
FGH = 104
Since BGK = FGH, we can substitute FGH with 104 in the first equation:
7w + 3 = 104
To solve for w, we can subtract 3 from both sides of the equation:
7w = 101
Finally, divide both sides of the equation by 7 to isolate w:
w = 101 / 7
So the value of w is w = 101/7, which is approximately 14.43.
fgk = 7w + 3 = 104/2,
7w + 3 = 52,
7w = 52 - 3,
7w = 49,
w = 7.