Question

Find x for the following circle. This is geometry.

Answer 1

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

    = $\frac{1}{2}$ (m larger arc - m smaller arc)

∵ The measure of the angle between the tangents is 50°

∴ 50 =  $\frac{1}{2}$ [(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°