Inscribed Angles and Arcs

This video tutorial covers the calculation of measures of arcs, inscribed angles, central angles, and angles of polygons when placed in a circle. It includes examples of right triangles, inscribed angles, and quadrilaterals, demonstrating how to solve for unknown values using these geometric principles. The tutorial concludes with a preview of the next lesson on calculating lengths of chords, diameters, radii, and tangents.

What is the relationship between a central angle and the arc it intercepts?

• The central angle is unrelated to the arc it intercepts.

• The central angle is double the arc it intercepts.

• The central angle is equal to the arc it intercepts.

• The central angle is half the arc it intercepts.

If a triangle is inscribed in a circle and one side is the diameter, what type of triangle is it?

• Equilateral triangle

• Isosceles triangle

• Right triangle

• Scalene triangle

How do you calculate the measure of an arc intercepted by an inscribed angle?

• Divide the inscribed angle by two

• Double the measure of the inscribed angle

• Add the inscribed angle to 90°

• Subtract the inscribed angle from 180°

What is the measure of an inscribed angle if the arc it intercepts measures 104°?

• 26°

• 208°

• 104°

• 52°

In a circle, if two inscribed angles intercept the same arc, what can be said about these angles?

• They are equal

• They are complementary

• They are supplementary

• They are unrelated

What must be true for a quadrilateral to be inscribed in a circle?

• All sides must be equal

• All angles must be right angles

• Opposite angles must be supplementary

• All angles must be equal

If an inscribed angle measures 79°, what is the measure of the arc it intercepts?

• 39.5°

• 79°

• 180°

• 158°

How do you find the measure of an arc if you know the measure of the inscribed angle?

• Subtract the inscribed angle from 180°

• Multiply the inscribed angle by 2

• Divide the inscribed angle by 2

• Add 90° to the inscribed angle

What is the sum of all arcs in a circle?

• 360°

• 720°

• 180°

• 540°

If a quadrilateral is inscribed in a circle, and one angle measures 113°, what is the measure of its opposite angle?

• 67°

• 47°

• 113°

• 82°