if m<DEG= 5x-4, m<GEF= 7x-8, m<DEH= 9y+5, find the values of x and y.
i know x=16 but i don't know how to find y.
how are the angles arranged?
That is, what is the order of D,F,G,H around point E?
Are there any right angles or straight angles in the picture?
There is no right or straight angles in the picture.
To find the value of y, we need to use the information provided about the angles.
Given that m<DEG = 5x - 4 and m<GEF = 7x - 8, we can set up an equation by equating these two angles:
5x - 4 = 7x - 8
Now, we can solve this equation to find the value of x:
5x - 7x = -8 + 4
-2x = -4
x = -4 / -2
x = 2
Therefore, x = 2.
To find the value of y, we will use the information that m<DEH = 9y + 5.
Given that x = 2, we substitute this into m<DEH:
m<DEH = 9y + 5
m<DEH = 9(2) + 5
m<DEH = 18 + 5
m<DEH = 23
Therefore, m<DEH = 23.
Now we can set up a new equation with m<DEH:
m<DEH = 23
9y + 5 = 23
Solving this equation will give us the value of y:
9y = 23 - 5
9y = 18
y = 18 / 9
y = 2
Therefore, y = 2.
In conclusion, the values of x and y are x = 2 and y = 2.