Question

Could someone please help me?

x =

100
120
140

Answer 1

x = 140

Explanation:

The secants exterior angle theorem states that when two secants (lines that intersect a circle at two points) intersect each other outside of the circle, then the absolute value of the difference divided by (2) equals the angle formed by the intersection of the two secants. One can apply this theorem here by stating the following, call the measure of the unknown arc (y);

`(30-y)/(2)=10`

Solve for (y) with inverse operations:

`(30-y)/(2)=10\\\\30-y=20\\\\y = 10`

When there is a diameter in a circle, the degree measure of the arc surrounding the diameter is (180). One can apply this here by stating the following:

`30 + x + 10 = 180`

Simplify,

`40 + x = 180`

Inverse operations,

`40+x=180\\\\x = 140`