Question

In ΔDEF, \overline{DF} DF is extended through point F to point G, \text{m}\angle FDE = (2x+4)^{\circ}m∠FDE=(2x+4) ∘ , \text{m}\angle DEF = (3x+3)^{\circ}m∠DEF=(3x+3) ∘ , and \text{m}\angle EFG = (7x-5)^{\circ}m∠EFG=(7x−5) ∘ . Find \text{m}\angle FDE.M∠FDE.

Answer 1

its 16

Explanation:

just did it

Answer 2

To find the measure of angle FDE in triangle DEF, we can set up an equation using the given information. By solving the equation, we find that the measure of angle FDE is 5.5°.

To find the measure of angle FDE, we can start by setting up an equation using the given information. Since angle FDE is the exterior angle at point F of triangle DEF, it is equal to the sum of the remote interior angles:

m∠FDE = m∠DEF + m∠EFG

Substituting the given expressions for the measures of angles DEF and EFG:

(2x+4) = (3x+3) + (7x-5)

Now we can solve the equation for x:

2x+4 = 3x+3 + 7x-5

Combine like terms:

2x+4 = 10x-2

Subtract 2x and add 2 to both sides:

6 = 8x

Divide both sides by 8:

x = 0.75

Now we can find the measure of angle FDE by substituting the value of x back into the expression for angle FDE:

m∠FDE = (2(0.75)+4) = 5.5°

The probable question may be:

In Delta DEF overline DF is extended through point F to point G, m∠ FDE=(2x+4)^circ m∠ DEF=(3x+3)^circ , and m∠ EFG=(7x-5)^circ . Find m∠ FDE