SOLUTION: Triangle DEF is an isosceles triangle. Find the value of x, then find the measure of angle D. And the numbers are (4x+1) at D (5x-4) at F and I am missing E and I need to find the

Click here to see ALL problems on Triangles

Question 1180465: Triangle DEF is an isosceles triangle. Find the value of x, then find the measure of angle D.
And the numbers are (4x+1) at D (5x-4) at F and I am missing E and I need to find the measurement for D
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Triangle DEF is an isosceles triangle.
Find the value of x, then find the measure of angle D.
And the numbers are (4x+1) at D (5x-4) at F
:
Assuming that D is the single angle and E * F are the equal angles of the isosceles triangle
:
D + E + F = 180
Substituting, find x
(4x+1) + (5x-4) + (5x-4) = 180
Combine like terms
4x + 5x + 5x + 1 - 4 - 4 = 180
14x - 7 = 180
14x = 180 + 7
14x = 187
x = 187/14
x = 13.357, seems like you should have an integer solution here, anyway
find D
4(13.357) + 1 = 54.428 degrees
:
:
Check this by finding the other two angles
5(13.357) - 4 = 62.785
total the angles
54.428 + 62.785 + 62.785 = 179.998 ~ 180

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The statement of the problem is incomplete; we don't know which two angles are congruent.

It is most likely that the measures given in terms of x for angles D and F imply that those are the two congruent angles.

Using that interpretation....

4x+1=5x-4
5 = x

The measure of angles D and F is 4(5)+1 = 21 degrees each.

From there determine the measure of angle E knowing that the sum of the three angles is 180 degrees.