10-3 & 10-4

You are looking for the angle measure of angle CAB in degrees. If you notice CAB is 17%. In a full circle there is 360°. This piece is 17%. 17% of 360°.

So you are going to multiply

360° • .17

So 360 x 0.17=?

DAG is the 18%, 7%, and 1% slices all together. So together it is 26%.

So 360 • 0.26 = ?

RQT goes from R to T the long way through Q. It is half the circle plus the extra 47°.

Angle QPR is a vertical angle to angle UPT. So those are congruent. And then to find angle RPS realize that angle RPS and the 55° angle and the 47° angle add up to 180°

The QS is those 2 pieces put together.

Find ZY.

If you add the 12 and 28 you will find the length of the radius of the circle. That is 40. So the radius of this circle is 40mi. If you draw the radius from W to Y it will be 40mi. You create a right triangle. The hypotenuse is 40. The shorter leg is 12. The longer leg is what we are looking for.

So it looks like this.

So setting up the Pythagorean Theorem it would be

x²+12²=40²

Solve for x. Then that is half of ZY. So double that number you get for x.

Since the angle where the x is an inscribed angle to that opens to the diameter it has to be half of 180. In other words it is 90°. So set

6x = 90 and solve for x.

Find the value of a.

Since both inscribed angles open to the same arc the 2 angles are congruent.