# 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 .

Q3:

In the given figure, find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

Find length to the nearest integer.

Q5:

Given that is tangent to the circle and that and lie on the circle, determine the value of to the nearest tenth.

Q6:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q7:

Find .

Q8:

Find .

• A
• B
• C
• D

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 .

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