Understanding Circle Arcs and Angles

In this video, the instructor explains how to find the measures of two arcs formed by tangents to a circle and an external angle of 84°. The process involves setting up an equation using the formula for the exterior angle, solving for the smaller arc, and then calculating the larger arc by subtracting the smaller arc from 360°. The video concludes with a recap of the solution.

What is the given external angle in the problem?

• 96°

• 90°

• 84°

• 72°

What is the total angle sum of a circle?

• 450°

• 360°

• 180°

• 270°

If the smaller arc is labeled as X, what is the expression for the larger arc?

• X - 84

• 360 - X

• 180 - X

• X + 84

What formula is used to relate the arcs and the exterior angle?

• (Larger Arc * Smaller Arc) / 2 = Exterior Angle

• (Larger Arc + Smaller Arc) / 2 = Exterior Angle

• (Larger Arc / Smaller Arc) / 2 = Exterior Angle

• (Larger Arc - Smaller Arc) / 2 = Exterior Angle

After simplifying the equation, what is the expression obtained?

• 180 - X = 84

• 360 - 2X = 84

• X + 180 = 84

• 2X - 180 = 84

What is the value of the smaller arc X?

• 264

• 84

• 96

• 180

What is the measure of the larger arc?

• 264

• 180

• 360

• 96

How do you find the larger arc once the smaller arc is known?

• Multiply the smaller arc by 2

• Divide the smaller arc by 2

• Subtract the smaller arc from 360

• Add 84 to the smaller arc

What is the final step in finding the arc measures?

• Add the arcs together

• Verify the sum of arcs equals 360

• Multiply the arcs by 2

• Subtract the arcs from 180