Answer:
1). x = 43
2). x = 15
Step-by-step explanation:
1. By the theorem of secants and intercepted arcs,
angle inscribed by the secant and tangent = \(\frac{1}{2}(\text{Difference of arcs}\)
52 = \(\frac{1}{2}(190-2x)\)
52×2 = (190 - 2x)
- 2x = 104 - 190
- 2x = - 86°
x = \(\frac{86}{2}=43\)
2. By the theorem of two intersecting chords inside a circle,
(5x - 6) = \(\frac{1}{2}(101+37)\)
5x - 6 = \(\frac{138}{2}=69\)
5x = 69 + 6
5x = 75
x = \(\frac{75}{5}\)
x = 15
