# Worksheet: Angles Formed by Lines Intersecting outside a Circle

In this worksheet, we will practice finding the measure of an angle that is formed by lines intersecting outside a circle.

**Q1: **

Given that is the measure of the major arc , find the value of .

**Q2: **

Find .

**Q4: **

Find length to the nearest integer.

**Q6: **

Given that , , , and , find the lengths of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q7: **

Find .

**Q9: **

In the figure, find the value of .

- A
- B
- C
- D

**Q10: **

Find .

**Q11: **

Given that and , find .

**Q12: **

Find the value of .

**Q13: **

Given that is a tangent to the circle below, find .

**Q14: **

Given that and are two tangents to the circle , and , determine .

**Q15: **

Given that , find .

**Q16: **

Lines and are tangent to circle . If , what is ?

**Q17: **

Given that is a diameter in the circle , is a tangent to the circle at , and , find .

**Q18: **

Given that , where and are tangent to the circle at and , find .

**Q19: **

In the figure, and are tangents to . What is ?

**Q20: **

is the regular pentagon drawn inside the circle , is a tangent to the circle at , and is a tangent to the circle at . Find .

**Q21: **

Circle has radius 65. Suppose is on a line and is perpendicular to . If what can be said of how lies with respect to the circle?

- A is outside of circle
- B is a tangent to circle
- C is a secant to circle

**Q22: **

In the figure, is a diameter of the circle . Given that , find .

**Q23: **

If , find .