Find 20-24 using the picture provide

20) MAD = 60°

21) <LPN = 57°

22) Second and third images, XY  is the tangent of circle Z

23) x = 11.2

Step-by-step explanation:

20)

<B = <C

11x - 3 = 8x + 15

3x = 18

x = 3

so

<B = <C = 11(3) - 3  = 33 - 3 = 30

mAD = 2(30) = 60

21)

a) <LPN = 1/2(360 - 102 - 144)

= 1/2(114)

= 57°

22)

The tangent to a circle is perpendicular to the radius at the point of tangency.

a)

(7+5)^2 = 7^2 + 10^2

(12)^2 = 49 + 100

144 ≠ 149

First image, XY is not tangent of circle Z

b)

20^2 = 12^2 + (8+8)^2

400 = 144 + 256

400 = 400

Second image, XY is  the tangent of circle Z

c)

(11.7 +7.8)^2 = 11.7^2 + 15.6^2

380.25 = 136.89 + 243.36

380.25 = 380.25

Third image, XY  is the tangent of circle Z

23)

x^2 = (8.4+5.6)^2 - (8.4)^2

x^2 = 196 - 70.56

x^2 = 125.44

x = 11.2