Answer:
∠MON = 57°
Explanation:
Given that OL and ON are perpendicular lines then ∠LON = 90° and
∠LOM + ∠MON = 90, substitute values
3x - 15 + 5x - 23 = 90, that is
8x - 38 = 90 ( add 38 to both sides )
8x = 128 ( divide both sides by 8 )
x = 16
Hence
∠MON = 5x - 23 = (5 × 16) - 23 = 80 - 23 = 57°