if m<GEF = 2x + 10, m<DEF = 5x- 10, and m<GED = 70, find m<GEF and m<DEF
no idea. If D is between G and F, then
GED+DEF=GEF, so
70+5x-10 = 2x+10
3x = -50
x = -17/3
Not likely.
If F is between D and G, then
DEF+GEF = GED
5x-10 + 2x+10 = 70
7x = 70
x = 10
DEF = 40
GEF = 30
Next time, describe the figure more clearly, eh?
To find m<GEF and m<DEF, we can use the relationships between angles within a triangle.
In this case, we need to focus on the relationship between the angles GEF, DEF, and GED in triangle GEF. The sum of the interior angles of a triangle is always 180 degrees.
So, we have the equation: m<GEF + m<DEF + m<GED = 180
Substituting in the given values:
2x + 10 + 5x - 10 + 70 = 180
Combining like terms:
7x + 70 = 180
Subtracting 70 from both sides:
7x = 110
Dividing both sides by 7:
x = 110/7
Now that we know the value of x, we can substitute it back into the equations for m<GEF and m<DEF.
For m<GEF:
m<GEF = 2x + 10 = 2(110/7) + 10
Simplifying:
m<GEF = 220/7 + 10
m<GEF = 220/7 + 70/7
m<GEF = 290/7
For m<DEF:
m<DEF = 5x - 10 = 5(110/7) - 10
Simplifying:
m<DEF = 550/7 - 10
m<DEF = 550/7 - 70/7
m<DEF = 480/7
Therefore, m<GEF is equal to 290/7 and m<DEF is equal to 480/7.