Answer:
The value of x is 9
Step-by-step explanation:
The measure of the exterior angle at a vertex of a triangle equals the sum of the measures of the two opposite interior angles to this vertex
In the given figure
∵ ∠DFG is an exterior angle at vertex F
∵ The angles of measures (5x - 7) and 89° are the opposite interior
angles to the vertex F
∴ m∠DFG = (5x - 7) + 89
∵ m∠DFG = 14x + 1
→ Substitute it in the equation above
∴ 14x + 1 = 5x - 7 + 89
→ Add the like terms in the right side
∵ 14x + 1 = 5x + 82
→ Subtract 1 from both sides
∵ 14x + 1 - 1 = 5x + 82 - 1
∴ 14x = 5x + 81
→ Subtract 5x from both sides
∴ 14x - 5x = 5x - 5x + 81
∴ 9x = 81
→ Divide both sides by 9
∴ x = 9
∴ The value of x is 9
