Final answer:
To find m∠FDE, we used the exterior angle theorem and solved the equation. The value of x was found to be 4, which gave m∠FDE = 12°, not matching any provided options. Please check the question for accuracy.
Step-by-step explanation:
We are given a triangle ΔDEF with DF extended to point G. The measures of the angles are given by m∠FDE = (2x + 4)°, m∠DEF = (3x + 3)°, and m∠EFG = (7x - 5)°. Since ∠EFG is an exterior angle at vertex F, we can use the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.
To find the value of x, we can set up the equation m∠EFG = m∠FDE + m∠DEF:
(7x - 5)° = (2x + 4)° + (3x + 3)°
Simplify and solve for x:
7x - 5 = 2x + 4 + 3x + 3
Solving the equation, x is equal to 4. Now, to find the measure of ∠FDE, we substitute x = 4 into the angle's expression:
m∠FDE = 2(4) + 4 = 8 + 4 = 12°, which is not one of the provided options. Therefore, please double-check the question for any possible typos or missing information before we proceed.