Answer: 48°
Explanation:
We know that the angles of a triangle are equal to 180 degrees when added together. Using this logic, we will create an equation to solve for x. Then we will substitute this value of x back into the expression for angle F.
Given:
E + D + F = 180°
Substitue:
(8x - 18)° + (6x - 4)° + (5x - 7)° = 180°
Reorder and combine like terms:
8x° + 6x° + 5x° - 18° - 4° - 7° = 180°
19x° - 29° = 180°
Add 29 to both sides of the equation:
19x° = 209°
Divide both sides of the equation by 19:
x = 11
Substitute this value of x into the expression for angle F:
(5x - 7)°
(5(11) - 7)°
(55 - 7)°
48°