Answer
68°
Step-by-step explanation
Given:
m ∠O = (4x)°, m ∠M = (8x - 24)°
From the diagram,
m ∠M + m ∠O = 180° (Opposite angles of a cyclic quadrilateral is supplementary).
⇒ (8x - 24)° + (4x)° = 180°
Remove the brackets
8x - 24 + 4x = 180
Collect the like terms together
8x + 4x = 180 + 24
12x = 204
Divide both sides by the coefficient of x
12x/12 = 204/12
x = 17
Now, the given m ∠NOP = 4x
Substitute x = 17 into m ∠NOP
⇒4 x 17 = 68°