Angle Relationships in Circles

This video tutorial covers angle relationships in circles, focusing on three theorems: 12.5.1, 12.5.2, and 12.5.3. Theorems explain how to calculate angle measures based on the position of the angle's vertex relative to the circle. The video also demonstrates how to find arc measures using these theorems and concludes with a preview of the next lesson on chord-chord, secant-secant, and secant-tangent product theorems.

What is the measure of an angle if its vertex is on the circle and it intercepts a 120-degree arc?

• 30 degrees

• 90 degrees

• 60 degrees

• 120 degrees

Using theorem 12.5.1, if a tangent and secant intersect on a circle, what is the relationship between the angle formed and its intercepted arc?

• The angle is unrelated to the intercepted arc

• The angle is twice the intercepted arc

• The angle is half the intercepted arc

• The angle is equal to the intercepted arc

If an angle's vertex is inside the circle and it intercepts arcs measuring 44 and 86 degrees, what is the angle's measure?

• 65 degrees

• 130 degrees

• 44 degrees

• 86 degrees

What theorem is used to find the measure of an angle with its vertex inside the circle?

• Theorem 12.5.1

• Theorem 12.5.2

• Theorem 12.5.3

• Theorem 12.5.4

How do you calculate the measure of an angle with its vertex outside the circle?

• Half the difference of intercepted arcs

• Half the sum of intercepted arcs

• Twice the intercepted arc

• The full intercepted arc

If an angle's vertex is outside the circle and it intercepts arcs measuring 202 and 78 degrees, what is the angle's measure?

• 62 degrees

• 40 degrees

• 100 degrees

• 124 degrees

What is the measure of arc AF if the total circle is 360 degrees and the other arcs measure 60, 160, and 48 degrees?

• 160 degrees

• 48 degrees

• 60 degrees

• 92 degrees

If the measure of arc ADB is 220 degrees, what is the measure of arc AD if arc DB is 160 degrees?

• 80 degrees

• 220 degrees

• 160 degrees

• 60 degrees

What is the measure of arc BE if arcs AB, AF, and FE measure 48, 86, and 110 degrees respectively?

• 110 degrees

• 244 degrees

• 48 degrees

• 116 degrees

What is the next topic after angle relationships in circles?

• Tangent-tangent product theorem

• Secant-tangent product theorem

• Secant-secant product theorem

• Chord-chord product theorem