Question

Angle measures and segment lengths. Algebra Find the value of each variable.

Answer 1

The value of x is 50

Explanation:

• A secant is a line that intersects a circle in exactly two points.

• When two secants intersect outside a circle then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs

In the given figure

∵ Two secants intersected outside the circle

∵ The measures of the intercepted arcs are 30° and 130°

∵ x is the measure of the angle formed between them

→ By using the fact above

∴ x =
`(1)/(2)` (130 - 30)

∴ x =
`(1)/(2)` (100)

∴ x = 50

∴ The value of x is 50