WEBVTT

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So we're told that ray OL
is perpendicular to ray ON.

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So OL is perpendicular to ON.

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So we know that this right
over here is a right angle,

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or it's a 90-degree angle.

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Then they tell us that
the measure of angle LOM

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is equal to 2x plus 46.

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So LOM-- so this angle
right over here--

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is equal to 2x plus 46.

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Then they tell us that
the measure of angle MON

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is equal to 3x minus 6.

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So this angle right
over here is 3x minus 6.

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And so they ask
us find angle MON.

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So we need to find this
angle right over here.

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And we'd be able to find
it if we knew what x is.

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If we knew what x is, then
it's going to be 3 times

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that minus 6.

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Now, the one thing
that we know is

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that if we add up
these two angles,

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these are adjacent angles.

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And their outside rays
form a right angle.

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So these two angles are going
to add up to 90 degrees.

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And I guess we can assume here
that we're dealing in degrees.

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So let's say that 2x
plus 46 plus 3x minus 6

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is going to add
up to 90 degrees.

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These two angles
are complementary.

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So it's going to add
up to 90 degrees,

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or it's going to add up to 90.

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And now, we just
have to simplify.

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We have 2 x's.

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We have another 3 x's.

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So you add those two, and
you're going to get 5 x's.

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And then you have 46.

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And you're going to subtract 6.

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So it's going to be
plus 40 is equal to 90.

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Subtract 40 from both sides.

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So let's do that.

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Subtract 40 from both sides.

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And on the left-hand side,
you're just left with a 5x.

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And on the right-hand side,
you're left with a 50.

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Now, just divide
both sides by 5.

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And we are left with
x is equal to 10.

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Now, our answer is not 10.

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We've just figured
out what x is.

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What they ask us for is what's
the measure of angle MON?

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Well, we already know that
the measure of angle MON

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is equal to 3x minus 6, which
is equal to 3 times 10 minus 6--

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I want to do that minus 6
in that green color-- which

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is equal to 24 degrees.