# Worksheet: Angles of Intersecting Lines in a Circle

In this worksheet, we will practice finding the measures of angles resulting from the intersection of two chords, two secants, or tangents and secants in a circle.

**Q2: **

In the given figure, . Determine .

**Q3: **

Determine .

**Q4: **

In the given figure, find .

**Q5: **

Find the value of .

**Q6: **

Given that , find .

**Q7: **

Find .

- A
- B
- C
- D
- E

**Q8: **

Find .

**Q9: **

Find .

- A
- B
- C
- D
- E

**Q10: **

Given that, in the shown figure, and , determine the value of .

**Q11: **

Given that , find the value of .

**Q12: **

Given that is a tangent to the circle, find .

**Q13: **

Find .

**Q14: **

The circle in the given figure has an arc with a measure of .

What is the measure of the central angle?

What is the measure of the inscribed angle?

What is the measure of the circumscribed angle?

**Q15: **

Find .

**Q16: **

Find the value of .

**Q17: **

Given that, in the shown figure, and , determine the value of .

**Q18: **

In the given figure, find .

**Q19: **

Find .

- A
- B
- C
- D
- E

**Q20: **

In the shown figure, is tangent to the circle, , , and . Determine the lengths of and .

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

**Q21: **

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

**Q22: **

The point is outside a circle with centre . The line between and intersects the circle at and , and the line between and meets the circle at points and . Given that and , find .

**Q23: **

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

**Q25: **

Find .