Lesson Worksheet: Angles of Tangency Mathematics • 11th Grade

In this worksheet, we will practice identifying the angle of tangency in a circle and find its measure using the measure of its subtended arc, inscribed angle, or central angle subtended by the same arc.


Given that οƒͺ𝐡𝐢 is a tangent to the circle below, find π‘šβˆ π΄π΅πΆ.


Find π‘šβˆ πΆπ΄π΅.


Given that οƒͺ𝐡𝐢 is a tangent to the circle, find π‘šβˆ π΄π΅πΆ.


Given that π‘šβˆ πΈπΆπ·=54∘ and π‘šβˆ πΉπ΅π·=78∘, find π‘₯ and 𝑦.

  • A54, 84
  • B48, 84
  • C78, 84
  • D78, 102
  • E54, 126


Find π‘šβˆ πΈπΆπ·.


Find π‘šβˆ πΈπ·πΆ.


Find π‘šβˆ π΅π΄πΆ.


⃖⃗𝐡𝐢 is tangent to the circle of center 𝑀 at 𝐡. Find π‘šβˆ π΄π΅πΆ.


Suppose that βƒ–οƒ©οƒ©οƒ©οƒ©οƒ©βƒ—π‘‹π‘Œ is a tangent to the circle with center 𝑀 at 𝐡, 𝐡𝐴βˆ₯𝑀𝐢, and π‘šβˆ π΄π΅π‘Œ=51.8∘. Find π‘šβˆ πΆπ΅π‘‹.


In the given figure, if 𝐴𝐷≠𝐴𝐡≠𝐡𝐢, which of the following is a tangent to the circle that passes through the vertices of the triangle 𝐴𝐡𝐸?

  • A𝐴𝐷
  • B𝐸𝐷
  • C𝐡𝐢
  • Dοƒͺπ΅π‘Œ
  • E𝐸𝐢

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