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.

Step-by-step explanation:

See the diagram attached:

In a triangle, the sum of interior angles is equal to the exterior angle.

According the diagram, the sum of interior angles is given as:

Sum of interior = <FDE+<DEF

Given

<FDE = 2x+4

<DEF = 3x+5

Sum of interior = 2x+4+3x+5

Sum of interior = 5x+9

Exterior angle = <EFG = 7x-5

Equate the interior to the exterior and calculate the value of x:

5x+9 = 7x-5

Collect like terms

5x-7x = -5-9

-2x = -14

x = -14/-2

x = 7

Next is to get <FDE:

<FDE = 2x+4

<FDE = 2(7)+4

<FDE = 14+4

<FDE = 18°

Hence the measure of <FDE is 18°