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Answer:
<h3>18°</h3>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°
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