[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.69,0:00:04.99,Default,,0000,0000,0000,,So we're told that ray OL\Nis perpendicular to ray ON.
Dialogue: 0,0:00:04.99,0:00:07.64,Default,,0000,0000,0000,,So OL is perpendicular to ON.
Dialogue: 0,0:00:07.64,0:00:10.02,Default,,0000,0000,0000,,So we know that this right\Nover here is a right angle,
Dialogue: 0,0:00:10.02,0:00:11.60,Default,,0000,0000,0000,,or it's a 90-degree angle.
Dialogue: 0,0:00:11.60,0:00:15.19,Default,,0000,0000,0000,,Then they tell us that\Nthe measure of angle LOM
Dialogue: 0,0:00:15.19,0:00:18.06,Default,,0000,0000,0000,,is equal to 2x plus 46.
Dialogue: 0,0:00:18.06,0:00:22.36,Default,,0000,0000,0000,,So LOM-- so this angle\Nright over here--
Dialogue: 0,0:00:22.36,0:00:24.94,Default,,0000,0000,0000,,is equal to 2x plus 46.
Dialogue: 0,0:00:28.10,0:00:31.00,Default,,0000,0000,0000,,Then they tell us that\Nthe measure of angle MON
Dialogue: 0,0:00:31.00,0:00:34.48,Default,,0000,0000,0000,,is equal to 3x minus 6.
Dialogue: 0,0:00:34.48,0:00:38.44,Default,,0000,0000,0000,,So this angle right\Nover here is 3x minus 6.
Dialogue: 0,0:00:38.44,0:00:40.73,Default,,0000,0000,0000,,And so they ask\Nus find angle MON.
Dialogue: 0,0:00:40.73,0:00:43.34,Default,,0000,0000,0000,,So we need to find this\Nangle right over here.
Dialogue: 0,0:00:43.34,0:00:45.38,Default,,0000,0000,0000,,And we'd be able to find\Nit if we knew what x is.
Dialogue: 0,0:00:45.38,0:00:47.50,Default,,0000,0000,0000,,If we knew what x is, then\Nit's going to be 3 times
Dialogue: 0,0:00:47.50,0:00:48.72,Default,,0000,0000,0000,,that minus 6.
Dialogue: 0,0:00:48.72,0:00:50.33,Default,,0000,0000,0000,,Now, the one thing\Nthat we know is
Dialogue: 0,0:00:50.33,0:00:52.02,Default,,0000,0000,0000,,that if we add up\Nthese two angles,
Dialogue: 0,0:00:52.02,0:00:53.71,Default,,0000,0000,0000,,these are adjacent angles.
Dialogue: 0,0:00:53.71,0:00:56.88,Default,,0000,0000,0000,,And their outside rays\Nform a right angle.
Dialogue: 0,0:00:56.88,0:01:00.13,Default,,0000,0000,0000,,So these two angles are going\Nto add up to 90 degrees.
Dialogue: 0,0:01:00.13,0:01:02.82,Default,,0000,0000,0000,,And I guess we can assume here\Nthat we're dealing in degrees.
Dialogue: 0,0:01:02.82,0:01:12.99,Default,,0000,0000,0000,,So let's say that 2x\Nplus 46 plus 3x minus 6
Dialogue: 0,0:01:12.99,0:01:17.41,Default,,0000,0000,0000,,is going to add\Nup to 90 degrees.
Dialogue: 0,0:01:17.41,0:01:19.61,Default,,0000,0000,0000,,These two angles\Nare complementary.
Dialogue: 0,0:01:19.61,0:01:21.83,Default,,0000,0000,0000,,So it's going to add\Nup to 90 degrees,
Dialogue: 0,0:01:21.83,0:01:23.16,Default,,0000,0000,0000,,or it's going to add up to 90.
Dialogue: 0,0:01:23.16,0:01:24.58,Default,,0000,0000,0000,,And now, we just\Nhave to simplify.
Dialogue: 0,0:01:24.58,0:01:25.46,Default,,0000,0000,0000,,We have 2 x's.
Dialogue: 0,0:01:25.46,0:01:26.69,Default,,0000,0000,0000,,We have another 3 x's.
Dialogue: 0,0:01:26.69,0:01:29.72,Default,,0000,0000,0000,,So you add those two, and\Nyou're going to get 5 x's.
Dialogue: 0,0:01:29.72,0:01:32.42,Default,,0000,0000,0000,,And then you have 46.
Dialogue: 0,0:01:32.42,0:01:33.71,Default,,0000,0000,0000,,And you're going to subtract 6.
Dialogue: 0,0:01:33.71,0:01:36.70,Default,,0000,0000,0000,,So it's going to be\Nplus 40 is equal to 90.
Dialogue: 0,0:01:39.22,0:01:41.55,Default,,0000,0000,0000,,Subtract 40 from both sides.
Dialogue: 0,0:01:41.55,0:01:42.45,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:01:42.45,0:01:45.06,Default,,0000,0000,0000,,Subtract 40 from both sides.
Dialogue: 0,0:01:45.06,0:01:49.14,Default,,0000,0000,0000,,And on the left-hand side,\Nyou're just left with a 5x.
Dialogue: 0,0:01:49.14,0:01:53.22,Default,,0000,0000,0000,,And on the right-hand side,\Nyou're left with a 50.
Dialogue: 0,0:01:53.22,0:01:55.95,Default,,0000,0000,0000,,Now, just divide\Nboth sides by 5.
Dialogue: 0,0:01:55.95,0:02:00.63,Default,,0000,0000,0000,,And we are left with\Nx is equal to 10.
Dialogue: 0,0:02:00.63,0:02:02.24,Default,,0000,0000,0000,,Now, our answer is not 10.
Dialogue: 0,0:02:02.24,0:02:04.28,Default,,0000,0000,0000,,We've just figured\Nout what x is.
Dialogue: 0,0:02:04.28,0:02:07.47,Default,,0000,0000,0000,,What they ask us for is what's\Nthe measure of angle MON?
Dialogue: 0,0:02:07.47,0:02:11.77,Default,,0000,0000,0000,,Well, we already know that\Nthe measure of angle MON
Dialogue: 0,0:02:11.77,0:02:23.30,Default,,0000,0000,0000,,is equal to 3x minus 6, which\Nis equal to 3 times 10 minus 6--
Dialogue: 0,0:02:23.30,0:02:27.43,Default,,0000,0000,0000,,I want to do that minus 6\Nin that green color-- which
Dialogue: 0,0:02:27.43,0:02:32.55,Default,,0000,0000,0000,,is equal to 24 degrees.