- [Voiceover] So we're told that angle A is
circumscribed about circle O.
So this is angle A right over here,
we're talking about this angle right over there.
And when they say it's circumscribed about circle O
that means that the two sides of the angle
they're segments that would be part of tangent lines,
so if we were to continue, so for example
that right over there, that line is tangent to the circle
and (mumbles)
and this line is also tangent to the circle.
So you see that the sides of angle A
are parts of those tangents, and points B and point C
are where those tangents actually sit on the circle.
So given all of that they're asking us
what is the measure of angle A,
so we're trying to figure this out right here
and I encourage you to pause the video
and figure it out on your own.
So the key insight here and there's multiple ways
that you could approach this is to realize,
that a radius is going to be perpendicular to a tangent
or a radius that intersects a tangent
is going to be perpendicular to it.
So let me label this,
so this is going to be a right angle
and this is going to be a right angle.
In any quadrilateral, the sum of the angles
are going to add up to 360 degrees,
and if you wonder where that comes from
well you can divide a quadrilateral into two triangles,
where the sum of all the interior angles
of a triangle are 180 and since you have two of them,
it's 360 degrees.
So this is 92 + 90 + 90 + question mark
is going to be equal to 360 degrees.
So let me write that down.
92 plus 90 plus 90 so plus 180.
Plus, let's just call this X. X degrees.
Plus X, they all have to add up to be 360 degrees
so let's see, we could subtract 180 from both sides
and so, if we do that we would have
92 plus X is equals to 180
and if we subtract 92 from both sides
we get X is equals to let's see 180 minus 90 would be 90
and then we're just going to subtract two more
so it's going to be X is equals to 88.
So the measure of angle A is 88 degrees.
Now let's do one more of these.
These are surprisingly fun. All right.
So it says, angle A is circumscribed about circle O,
we have seen that before in the last question
and they said what is the measure of angle D.
So we want to find, let me make sure I'm on the right layer.
We want to find the measure of that angle
and let's call that, let's call that x again.
So what can we figure out?
Well just like in the last question
we have a quadrilateral here, quadrilateral A, B, O, C
and we know two of the angles,
we know this is going to be a right angle
we have a radius intersecting with a tangent,
or part of a tangent I guess you could say.
And then this would be a right angle
and so by the same logic as we saw in the last question,
this angle, plus this angle, plus this angle,
plus the central angle are going to add up to 360 degrees.
So let's call the measure of the central angle
let's call that Y over there.
So we have Y plus 80 degrees or
we'll just assume everything is in degrees,
so Y plus 80 plus 90 plus 90, so I could say
plus another 180 is going to be equal to 360 degrees
sum of the interior angles of a quadrilateral.
And so let's see you have, we could have
Y plus 80 is equal to 180,
if I just subtract 180 from both sides
if I subtract 80 from both sides, we get Y is equal to 100
or the measure of this is 100,
the measure of this interior angle
right over here is 100 degrees,
which also tells us that the measure of this arc
cause that interior angle intercepts...
intercepts arc C, B, right over here,
that tells us that the measure
of arc C, B, is also 100 degrees.
And so if we're trying to find this angle,
the measure of angle D, that's an inscribed angle
that intercepts the same arc.
And we've seen in previous videos that an inscribed angle
that intercepts that arc is going to have
half the arc's measure.
So if this is a 100 degree measured arc,
then the measure of this angle
right over here is going to be 50 degrees.
So the measure of angle D is 50 degrees.
And we are done.