Answer:
128°
Explanation:
You want the missing angle in the octagon with interior angles x, 106°, 144°, 129°, and 70°; exterior acute angles of 45° and 31°; and exterior obtuse angle 141°.
Angle sum theorem
The sum of angles in the n = 8-sided polygon will be 180°(n -2) = 1080°
The interior angles are the supplement of exterior acute angles. The interior reflex angle is the difference between 360° and the exterior obtuse angle. This means we have ...
x +(180 -45) +106 +144 +(180 -31) +129 +(360 -141) +70 = 1080
x -45 +106 +144 -31 +129 -141 +70 = 360 . . . . . . subtract 720
x + 232 = 360
x = 128
The missing angle is 128°.