# 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.

Q1:

Find the value of . 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 . Q8:

Find . Q9:

Find . 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 . 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 center . 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 . Q24:

Find . Q25:

Find . 