Answer:
x ≈ 30.8
Step-by-step explanation:
You want the value of x if the measure of an interior angle of a regular octagon is (4x +12)°.
The sum of interior angles of an n-gon is 180°×(n -2), where n is the number of sides. An octagon has 8 sides, so the sum of angles is ...
180°×(8 -2) = 1080°
The angles of a regular n-gon are congruent, so one interior angle of a regular octagon is ...
1080°/8 = 135°
The given angle expression is equal to 135°, so we have ...
(4x +12)° = 135°
4x = 123 . . . . . . . divide by ° and subtract 12
x = 30.75 . . . . . . divide by the coefficient of x
The value of x is about 30.8.
