Question

What is the value of a + b + c? You may assume that the ray is tangent to the circle.

133
47
86
150

Answer 1

When you have an inscribed angle, how does its measured compare to the measure of the intercepted arc?

For example, what is x below?

Answer 2

It's cut in half

Answer 3

Correct. In the example above, x = 15.

Answer 4

Now let's look at your problem.

Answer 5

What is c?

Answer 6

43

Answer 7

Good. One down, two to go.
What is a?

Answer 8

27

Answer 9

Good again. Two down, one to go.

Answer 10

Now you need another piece of information.

Answer 11

A tangent to a circle intersects a radius at the point of tangency a right angle.

Answer 12

Of angles a, b, and c, which two add up to a right angle?

Answer 13

a and b ?

Answer 14

Correct.
You know the measure of a; you know a and b add up to 90. Can you find b?

Answer 15

yes it'd be 63

Answer 16

Good.
Now add up a, b, and c.

Answer 17

133

ooh okay I get it

Answer 18

That's it.