Answer:
x = 130°
Step-by-step explanation:
- In a circle, if two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
- The measure of a circle is 360°
∵ The tangents divide the circle into two arcs
∴ The sum of the measures of the two arcs is 360°
∵ The measure of the smaller arc is x°
- To find the measure of the larger arc subtract x from 360
∴ The measure of the larger arc is (360 - x)°
∵ The two tangents intersected out the circle
∵ They formed an angle of measure 50° between them
- By using the first rule above
∵ The measure of the angle between the two tangents
= [tex]\frac{1}{2}[/tex] (m larger arc - m smaller arc)
∵ The measure of the angle between the tangents is 50°
∴ 50 = [tex]\frac{1}{2}[/tex] [(360 - x) - x]
- Multiply both sides by 2
∴ 100 = (360 - x) - x
- Add the like terms in the right hand side
∴ 100 = 360 - 2 x
- Add 2 x to both sides
∴ 2 x + 100 = 360
- Subtract 100 from both sides
∴ 2 x = 260
- divide both sides by 2
∴ x = 130°
