Question

what is the arc measure of YZ in degrees

Answer 1

Answer:

59°

Step-by-step 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°