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so we're told that rayo L is perpendicular ray o n so oh L is perpendicular to n so we know that this right over here is a right angle or it's a 90-degree angle then they tell us that the measure of angle LOM is equal to 2x plus 46 so L o M so this angle right over here is equal to 2x plus 46 and then this angle then they tell us that the measure of angle mo n is equal to 3x minus 6 so M o n so this angle right over here is 3 X minus 6 and so they asked us find angle mo n so we need to find this angle right over here and we'd be able to find it if we knew what X is if we knew what X is and assumed to be 3 times that minus 6 now the one thing that we know is that if we add up these two angles these are adjacent angles and they're outside Ray's form a right angle so these two angles are going to add up to 90 degrees and I guess we can assume here that we're dealing in degrees so let's say that 2 X 2 X plus 46 plus plus 3 X minus 6 is going to add up to 90 degrees these two angles are complementary so it's going to add up to 90 degrees or it's going to add up to 90 and now we just have to simplify we have 2 X's so we have another 3 X's so you add those two you're going to get 5 X's and then you have 46 and you're going to subtract 6 so it's going to be plus 40 is equal to 90 is equal to 90 subtract 40 from both sides let's do that subtract 40 from both sides and on the left hand side you're just left with a 5x and on the right hand side you are left with a 50 now just divide both sides by 5 and we are left with X is equal to 10 now our answer is not 10 we've just figured out what X is we asked us for is what's the measure of angle mo n well we already know that the measure of angle M o n is equal to 3x - six which is equal to 3 times 10 3 times 10 minus 6 that I wanted at minus 6 in that green color minus 6 which is equal to 24 24 degrees