Angles in Circles and Arcs

This video tutorial covers various aspects of circle geometry, focusing on calculating angles and arcs. It begins with central angles and their congruence with intercepted arcs, then moves to inscribed angles and properties of quadrilaterals in circles. The tutorial also explains how to find angles inside and outside circles using intercepted arcs, and tackles complex problems involving linear pairs and central angles. The session concludes with final angle problems and a review of key concepts.

What is the measure of a central angle if the intercepted arc is 135 degrees?

• 90 degrees

• 135 degrees

• 180 degrees

• 45 degrees

If an inscribed angle intercepts an arc of 70 degrees, what is the measure of the inscribed angle?

• 105 degrees

• 35 degrees

• 140 degrees

• 70 degrees

In a quadrilateral inscribed in a circle, if one angle is 80 degrees, what is the measure of its opposite angle?

• 90 degrees

• 180 degrees

• 100 degrees

• 80 degrees

How do you find the measure of an angle inside a circle that is not at the center?

• Divide intercepted arcs by two

• Multiply intercepted arcs

• Add intercepted arcs and divide by two

• Subtract intercepted arcs

What is the formula to find an exterior angle using arcs?

• Big arc times small arc

• Big arc plus small arc divided by two

• Big arc minus small arc divided by two

• Big arc divided by small arc

If a circle has a total of 360 degrees, and you subtract arcs of 60, 100, and 150 degrees, what is the remaining arc?

• 100 degrees

• 60 degrees

• 150 degrees

• 50 degrees

What is the measure of an angle that forms a linear pair with a 156-degree angle?

• 24 degrees

• 156 degrees

• 180 degrees

• 90 degrees

If two angles inside a circle are 54 and 48 degrees, what is the average angle?

• 102 degrees

• 51 degrees

• 54 degrees

• 48 degrees

What is the measure of an inscribed angle if the intercepted arc is 162 degrees?

• 41 degrees

• 81 degrees

• 324 degrees

• 162 degrees

How do you find the measure of an inscribed angle if you know the rest of the circle's arcs?

• Multiply by two

• Divide by 360

• Add to 360 and divide by two

• Subtract from 360 and divide by two