Question

What is the arc measure of YZ in degrees

Answer 1

59°

Explanation:

First we find the value of
`w` remembering that the angle that is formed in a straight line (in the diameter of the circle) is 180 °, so the sum :

`(11w)+(5w+4)`

must be equal to 180°:

`11w+5w+4=180`

and we add the two terms with w:

`16w+4=180`

we move the +4 in the left as a -4 to the right side:

`16w=180-4\\16w=176`

and next we divide by 16:

`w=176/16\\w=11`

And now that we know the value of
`w`, we can find the measure of the arc YZ:

`YZ=5w+4`

substituting
`w=11`

`YZ=5(11)+4\\YZ=55+4\\YZ=59`

The measure of YZ is 59°