0:00:00.690,0:00:04.990
So we're told that ray OL[br]is perpendicular to ray ON.

0:00:04.990,0:00:07.640
So OL is perpendicular to ON.

0:00:07.640,0:00:10.020
So we know that this right[br]over here is a right angle,

0:00:10.020,0:00:11.600
or it's a 90-degree angle.

0:00:11.600,0:00:15.190
Then they tell us that[br]the measure of angle LOM

0:00:15.190,0:00:18.060
is equal to 2x plus 46.

0:00:18.060,0:00:22.360
So LOM-- so this angle[br]right over here--

0:00:22.360,0:00:24.937
is equal to 2x plus 46.

0:00:28.100,0:00:31.000
Then they tell us that[br]the measure of angle MON

0:00:31.000,0:00:34.480
is equal to 3x minus 6.

0:00:34.480,0:00:38.440
So this angle right[br]over here is 3x minus 6.

0:00:38.440,0:00:40.730
And so they ask[br]us find angle MON.

0:00:40.730,0:00:43.339
So we need to find this[br]angle right over here.

0:00:43.339,0:00:45.380
And we'd be able to find[br]it if we knew what x is.

0:00:45.380,0:00:47.505
If we knew what x is, then[br]it's going to be 3 times

0:00:47.505,0:00:48.720
that minus 6.

0:00:48.720,0:00:50.330
Now, the one thing[br]that we know is

0:00:50.330,0:00:52.020
that if we add up[br]these two angles,

0:00:52.020,0:00:53.710
these are adjacent angles.

0:00:53.710,0:00:56.880
And their outside rays[br]form a right angle.

0:00:56.880,0:01:00.130
So these two angles are going[br]to add up to 90 degrees.

0:01:00.130,0:01:02.820
And I guess we can assume here[br]that we're dealing in degrees.

0:01:02.820,0:01:12.990
So let's say that 2x[br]plus 46 plus 3x minus 6

0:01:12.990,0:01:17.410
is going to add[br]up to 90 degrees.

0:01:17.410,0:01:19.610
These two angles[br]are complementary.

0:01:19.610,0:01:21.830
So it's going to add[br]up to 90 degrees,

0:01:21.830,0:01:23.164
or it's going to add up to 90.

0:01:23.164,0:01:24.580
And now, we just[br]have to simplify.

0:01:24.580,0:01:25.460
We have 2 x's.

0:01:25.460,0:01:26.690
We have another 3 x's.

0:01:26.690,0:01:29.720
So you add those two, and[br]you're going to get 5 x's.

0:01:29.720,0:01:32.419
And then you have 46.

0:01:32.419,0:01:33.710
And you're going to subtract 6.

0:01:33.710,0:01:36.700
So it's going to be[br]plus 40 is equal to 90.

0:01:39.220,0:01:41.550
Subtract 40 from both sides.

0:01:41.550,0:01:42.450
So let's do that.

0:01:42.450,0:01:45.060
Subtract 40 from both sides.

0:01:45.060,0:01:49.140
And on the left-hand side,[br]you're just left with a 5x.

0:01:49.140,0:01:53.220
And on the right-hand side,[br]you're left with a 50.

0:01:53.220,0:01:55.950
Now, just divide[br]both sides by 5.

0:01:55.950,0:02:00.630
And we are left with[br]x is equal to 10.

0:02:00.630,0:02:02.240
Now, our answer is not 10.

0:02:02.240,0:02:04.280
We've just figured[br]out what x is.

0:02:04.280,0:02:07.470
What they ask us for is what's[br]the measure of angle MON?

0:02:07.470,0:02:11.770
Well, we already know that[br]the measure of angle MON

0:02:11.770,0:02:23.300
is equal to 3x minus 6, which[br]is equal to 3 times 10 minus 6--

0:02:23.300,0:02:27.430
I want to do that minus 6[br]in that green color-- which

0:02:27.430,0:02:32.550
is equal to 24 degrees.