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 = [tex]\frac{1}{2}(\text{Difference of arcs}[/tex]
52 = [tex]\frac{1}{2}(190-2x)[/tex]
52×2 = (190 - 2x)
- 2x = 104 - 190
- 2x = - 86°
x = [tex]\frac{86}{2}=43[/tex]
2. By the theorem of two intersecting chords inside a circle,
(5x - 6) = [tex]\frac{1}{2}(101+37)[/tex]
5x - 6 = [tex]\frac{138}{2}=69[/tex]
5x = 69 + 6
5x = 75
x = [tex]\frac{75}{5}[/tex]
x = 15
