Example using algebra to find measure of supplementary angles

We're told that the measure
of angle QPR-- so that's

this angle right over
here-- is 2x plus 122.

And I'll assume that
these are in degrees.

So it's 2x plus 122 degrees.

And the measure of
angle RPS-- so that's

this angle right over here--
is 2x plus 22 degrees.

And they ask us to find
the measure of angle RPS.

So we need to figure out
this right over here.

So we would be able
to figure that out

if we just knew what x is.

And lucky for us, we
can use the information

given to solve for
x and then figure

out what 2 times x plus 22 is.

And the main big idea here,
the thing that pops out here,

is that the outside rays
for both of these angle

form a line.

These two angles form a line.

You could say that
they are supplementary.

Both of these angles
are supplementary.

2x plus 22 plus another 2x plus
122 is going to add up to 180.

We know that this entire angle
right over here is 180 degrees.

So we can say that the measure
of angle QPR, this angle

right over here, 2x plus
122, plus the green angle,

plus angle RPS-- so
plus 2x plus 22-- is

going to be equal
to 180 degrees.

And now we can start
simplifying this.

We have two x's.

We have another two x's.

So those are going
to add up to be 4x.

And then we have 122 plus 22.

So that's going to be 144.

And the sum of
those two are going

to be equal to 180 degrees.

We can subtract 144
from both sides.

On the left-hand
side, we're just

going to be left with a
4x, this 4x right here.

And on the right-hand
side, we're

going to have-- let's see,
if we were subtracting 140,

we would have 40 left.

And then we have to
subtract another 4,

so it's going to be 36.

Divide both sides by 4,
and we get x is equal to 9.

Now remember,
we're not done yet.

They didn't say solve for x.

They said find the measure of
angle RPS, which is 2 times

x plus 22 or 2 times
9 plus 22, which

is 18 plus 22, which
is equal to 40.

So the measure of angle
RPS is 40 degrees.