Angles and Arcs in Circles

This lesson covers angles inside and outside of circles, focusing on three main theorems: the intersecting chords angle theorem, the secant-secant theorem, and the tangent-chord theorem. Each theorem is explained with examples, demonstrating how to calculate angles and arcs using these formulas. The lesson concludes with a motivational message encouraging students to appreciate their learning journey.

What is the main focus of lesson 9.2?

• Angles in quadrilaterals

• Angles in polygons

• Angles inside and outside of circles

• Angles in triangles

Which theorem is used when you have two intersecting chords?

• Tangent-Secant Theorem

• Secant-Secant Theorem

• Intersecting Chords Angle Theorem

• Tangent-Chord Theorem

What is a chord in a circle?

• A line that touches the circle at one point

• A line with endpoints outside the circle

• A line with one endpoint on the circle

• A line with endpoints on the circle

How do you calculate the angle formed by two intersecting chords?

• Divide the arcs and add two

• Multiply the arcs and divide by two

• Subtract the arcs and divide by two

• Add the arcs and divide by two

If intercepted arcs are 60° and 80°, what is the angle formed by the intersecting chords?

• 70°

• 80°

• 90°

• 100°

In the example problem, what is the value of angle AED?

• 75°

• 80°

• 70°

• 60°

What is the value of arc GH in the example problem?

• 60°

• 65°

• 70°

• 75°

What do you need to use the Secant-Secant Theorem?

• Two secants

• A tangent and a chord

• Two chords

• Two tangents

How is the angle formed by two secants calculated?

• Multiply the arcs and divide by two

• Divide the arcs and add two

• Subtract the arcs and divide by two

• Add the arcs and divide by two

In the example, if the big arc is 110° and the small arc is 50°, what is the angle?

• 50°

• 40°

• 30°

• 20°