1. Find the value of x in the figure below. Show all steps. (Left) 2. Find the value of x in the figure below. Show all steps. (Right) Please show all of the steps. Thank you

Question

asked Jan 15, 2017 116k views

2 Answers

Ptkato · Answer 1 · 2017-01-20T23:05:22+0000

Answer:

1). x = 43

2). x = 15

Explanation:

1. By the theorem of secants and intercepted arcs,

angle inscribed by the secant and tangent =
$(1)/(2)(\text{Difference of arcs}$

52 =
(1)/(2)(190-2x)

52×2 = (190 - 2x)

- 2x = 104 - 190

- 2x = - 86°

x =
(86)/(2)=43

2. By the theorem of two intersecting chords inside a circle,

(5x - 6) =
(1)/(2)(101+37)

5x - 6 =
(138)/(2)=69

5x = 69 + 6

5x = 75

x =
(75)/(5)

x = 15