1 00:00:00,690 --> 00:00:04,990 So we're told that ray OL is perpendicular to ray ON. 2 00:00:04,990 --> 00:00:07,640 So OL is perpendicular to ON. 3 00:00:07,640 --> 00:00:10,020 So we know that this right over here is a right angle, 4 00:00:10,020 --> 00:00:11,600 or it's a 90-degree angle. 5 00:00:11,600 --> 00:00:15,190 Then they tell us that the measure of angle LOM 6 00:00:15,190 --> 00:00:18,060 is equal to 2x plus 46. 7 00:00:18,060 --> 00:00:22,360 So LOM-- so this angle right over here-- 8 00:00:22,360 --> 00:00:24,937 is equal to 2x plus 46. 9 00:00:28,100 --> 00:00:31,000 Then they tell us that the measure of angle MON 10 00:00:31,000 --> 00:00:34,480 is equal to 3x minus 6. 11 00:00:34,480 --> 00:00:38,440 So this angle right over here is 3x minus 6. 12 00:00:38,440 --> 00:00:40,730 And so they ask us find angle MON. 13 00:00:40,730 --> 00:00:43,339 So we need to find this angle right over here. 14 00:00:43,339 --> 00:00:45,380 And we'd be able to find it if we knew what x is. 15 00:00:45,380 --> 00:00:47,505 If we knew what x is, then it's going to be 3 times 16 00:00:47,505 --> 00:00:48,720 that minus 6. 17 00:00:48,720 --> 00:00:50,330 Now, the one thing that we know is 18 00:00:50,330 --> 00:00:52,020 that if we add up these two angles, 19 00:00:52,020 --> 00:00:53,710 these are adjacent angles. 20 00:00:53,710 --> 00:00:56,880 And their outside rays form a right angle. 21 00:00:56,880 --> 00:01:00,130 So these two angles are going to add up to 90 degrees. 22 00:01:00,130 --> 00:01:02,820 And I guess we can assume here that we're dealing in degrees. 23 00:01:02,820 --> 00:01:12,990 So let's say that 2x plus 46 plus 3x minus 6 24 00:01:12,990 --> 00:01:17,410 is going to add up to 90 degrees. 25 00:01:17,410 --> 00:01:19,610 These two angles are complementary. 26 00:01:19,610 --> 00:01:21,830 So it's going to add up to 90 degrees, 27 00:01:21,830 --> 00:01:23,164 or it's going to add up to 90. 28 00:01:23,164 --> 00:01:24,580 And now, we just have to simplify. 29 00:01:24,580 --> 00:01:25,460 We have 2 x's. 30 00:01:25,460 --> 00:01:26,690 We have another 3 x's. 31 00:01:26,690 --> 00:01:29,720 So you add those two, and you're going to get 5 x's. 32 00:01:29,720 --> 00:01:32,419 And then you have 46. 33 00:01:32,419 --> 00:01:33,710 And you're going to subtract 6. 34 00:01:33,710 --> 00:01:36,700 So it's going to be plus 40 is equal to 90. 35 00:01:39,220 --> 00:01:41,550 Subtract 40 from both sides. 36 00:01:41,550 --> 00:01:42,450 So let's do that. 37 00:01:42,450 --> 00:01:45,060 Subtract 40 from both sides. 38 00:01:45,060 --> 00:01:49,140 And on the left-hand side, you're just left with a 5x. 39 00:01:49,140 --> 00:01:53,220 And on the right-hand side, you're left with a 50. 40 00:01:53,220 --> 00:01:55,950 Now, just divide both sides by 5. 41 00:01:55,950 --> 00:02:00,630 And we are left with x is equal to 10. 42 00:02:00,630 --> 00:02:02,240 Now, our answer is not 10. 43 00:02:02,240 --> 00:02:04,280 We've just figured out what x is. 44 00:02:04,280 --> 00:02:07,470 What they ask us for is what's the measure of angle MON? 45 00:02:07,470 --> 00:02:11,770 Well, we already know that the measure of angle MON 46 00:02:11,770 --> 00:02:23,300 is equal to 3x minus 6, which is equal to 3 times 10 minus 6-- 47 00:02:23,300 --> 00:02:27,430 I want to do that minus 6 in that green color-- which 48 00:02:27,430 --> 00:02:32,550 is equal to 24 degrees.