Question

Would appreciate the help

Answer 1

Answer:

x° = 37°

Step-by-step explanation:

* Lets revise some facts of a circle

- The secant is a line intersect the circle in two points

- If two secants intersect each other in a point outside the circle,

 then the measure of the angle between them is half the difference

 of the measures of their intercepted arcs

* Now lets solve the problem

- There is a circle

- Two secants of this circle intersect each other in a point outside

  the circle

∴ The measure of the angle between them = 1/2 the difference of the

  measures of their intercepted arcs

∵ The measure of the angle between them is x°

∵ The measures of their intercepted arcs are 26° and 100°

- Use the rule above to find x

∴ x° = 1/2 [ measure of the large arc - measure of small arc]

∵ The measure of the large arc is 100°

∵ The measure of the small arc is 26°

∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°

∴ x° = 37°