Question

∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132°, what is the measure of ∠ABD?

Answer 1

Answer:

measure of ∠ABD = 42°

Step-by-step explanation:

Angle Formed by Tangent and Secant = (1/2)*(difference of Intercepted Arcs)

In this case the intercepted arcs are: minor arc AC and minor arc AD. Let´s first find minor arc AD, we know that:

minor arc AC + minor arc CD + minor arc AD = 360°

Then,

minor arc AD = 360° - minor arc AC - minor arc CD

minor arc AD = 360° - 72° - 132°

minor arc AD = 156°

Replacing in the aforementioned formula:

Angle Formed by Tangent and Secant = (1/2)*(difference of Intercepted Arcs)

∠ABD = (1/2)*(minor arc AD - minor arc AC)

∠ABD = (1/2)*(156° - 72°)

∠ABD = 42°