Angles and Arcs in Circles

The video tutorial explains how to calculate angles in different geometric scenarios. It covers three main cases: an angle inside a circle not at the center, an angle outside a circle using the difference of arcs, and an angle on a tangent line using the linear pair property. Each section provides step-by-step calculations and rules for determining the angles based on given arc measurements.

What is the formula to find an angle within a circle that is not at the center or inscribed?

• Multiply the intercepted arcs and divide by two

• Subtract the intercepted arcs and divide by two

• Add the intercepted arcs and multiply by two

• Add the intercepted arcs and divide by two

If the intercepted arcs are 160 and 50, what is the angle within the circle?

• 115 degrees

• 110 degrees

• 120 degrees

• 105 degrees

What is the rule for finding an exterior angle when given a big arc and a small arc?

• Big Arc times Small Arc divided by 2

• Small Arc minus Big Arc divided by 2

• Big Arc minus Small Arc divided by 2

• Big Arc plus Small Arc divided by 2

If the exterior angle is 30 and the small arc is 47, what is the big arc?

• 127

• 117

• 137

• 107

How do you solve for an unknown arc using the exterior angle rule?

• Add the exterior angle to the small arc

• Subtract the exterior angle from the small arc

• Multiply the exterior angle by the small arc

• Use cross multiplication after setting up the equation

What is the value of the unknown arc if the equation is set up as x - 47 divided by 2 equals 30?

• 127

• 97

• 117

• 107

Where does the vertex lie in a linear pair of angles on a circle?

• On the circle

• At the center of the circle

• Inside the circle

• Outside the circle

If one angle of a linear pair is 156 degrees, what is the other angle?

• 44 degrees

• 34 degrees

• 24 degrees

• 54 degrees

What is the sum of angles in a linear pair?

• 270 degrees

• 180 degrees

• 360 degrees

• 90 degrees

What is the relationship between angles in a linear pair?

• They are equal

• They are perpendicular

• They are supplementary

• They are complementary