This angle would have been slightly smaller than the first one.

This angle plus this angle is going to be equal to this angle.

Or this angle plus this angle plus this angle is equal to 180.

Then this angle, this interior angle right over here

We know this angle and we know this angle.

So that means that this angel, is equal to this angle, is equal to that angle

So this green angle plus this purple angle is equal to 180.

This angle right over here is going to be equal to that angle over there

And this right over here, this little marks says that this angle is equal to this angle is equal to this angle.

This angle, this whole angle is 180 degrees.

And we also we make this angle is equal to that angle.

How do we know that this angle is equal to this angle?

So, that angle is equal to that angle and that ABD, which is this angle is congruent to DCA which is that angle over here

This angle is equal to this vertical angle, is equal to its vertical angle right over here and that this angle is equal to this angle that is opposite the intersection right over here.

Well, if this angle is y, then this angle is opposite to y.

We'll this right here is equal to 92 degrees, and this angle right here is vertical with that angle.

And then this angle and this angle.

This angle is going to be congruent to that angle

That's angle 1 and that's angle 2.

This angle is the same as this angle, so it is also 120 degrees.

This angle right here.

This angle.

This angle right over there

Because this angle plus this magenta angle is going to equal the whole circle.

Angle BDC over here, it is an alternate interior angle with this angle right over here with that angle right over there

So if this is angle A, this is angle B, and then let's call this angle C.

Now if this angle is theta, what's this angle going to be?

And by the same argument, this angle is going to be congruent to that angle.

This angle right here is opposite to it, so this angle right here is going to be 101 degrees.

But thats also going on over here, this angle is equal to this angle is equal to this angle. they all have to be 60degrees.

And so, if this angle is congruent to that angle, that angle is congruent to that angle, then they're congruent to each other

We also know since this angle corresponds with this angle, this angle will also be 110 degrees.

If we knew that this angle is equal to that angle and that angle is equal to that angle, we'd be done.

Angle CBE, which is this angle right over here, is equal to angle DBA and sometimes you might see that shown like this so angle CBE, that's its measure, and you would say that this measure right over here is the exact same amount.

The world looks better from this angle.

So this angle is psi, this angle right here is theta.

And then finally, of course, this angle and this angle will also be the same.

So this pink angle theta plus this green angle must be equal to 90 degrees

Now this angle corresponds to that angle, but they're not equal.

It's congruent to this angle here.

That's a very complicated way of saying this orange angle and this magenta angle right here.

So whatever angle this green angle is, this angle is going to be as well

This larger angle right here.

That one right over there.

This is angle y.