Answer:
m < FGN = 88°
Explanation:
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).
Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:
The following equality statement can be established according to the exterior angle theorem:
m < E + m < F = m <FGN
38 + 6x - 10 = 7x + 18
Combine like terms:
28 + 6x = 7x + 18
Subtract 6x from both sides:
28 + 6x - 6x = 7x - 6x + 18
28 = x + 18
Subtract 18 from both sides:
28 - 18 = x + 18 - 18
10 = x
Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.
m < E + m < F = m <FGN
38° + (6x - 10)° = (7x + 18)°
38 + 6(10) - 10 = 7(10) + 18
38 + 60 - 10 = 70 + 18
88 = 88 (True statement).
Therefore, m < FGN = 88°