Angles Subtended by Arcs

The video tutorial covers the second problem from a 15-day math challenge, focusing on circle geometry. It explains the property of angles subtended by arcs at the center and circumference of a circle. The tutorial solves three problems using this property, calculating angles for different arcs and discussing cyclic quadrilaterals. The video concludes with a promise of more math content.

What is the main property of circles used in the problems discussed in the video?

• The radius is half the diameter.

• The angle subtended by an arc at the center is twice the angle subtended at the circumference.

• The diameter is the longest chord in a circle.

• The sum of angles in a triangle is 180 degrees.

If an arc subtends an angle of 80 degrees at the center, what is the angle subtended at the circumference?

• 40 degrees

• 80 degrees

• 20 degrees

• 160 degrees

What is the angle subtended at the circumference by an arc that subtends 70 degrees at the center?

• 35 degrees

• 70 degrees

• 140 degrees

• 105 degrees

If an arc subtends 160 degrees at the center, what is the angle subtended at the circumference?

• 80 degrees

• 40 degrees

• 160 degrees

• 100 degrees

In a cyclic quadrilateral, what is the sum of the opposite angles?

• 270 degrees

• 180 degrees

• 90 degrees

• 360 degrees

If angle Z in a cyclic quadrilateral is 80 degrees, what is the measure of the opposite angle W?

• 100 degrees

• 80 degrees

• 180 degrees

• 90 degrees

What is the angle Y if the arc subtends 120 degrees at the center?

• 120 degrees

• 30 degrees

• 60 degrees

• 90 degrees

What is the value of angle X if the arc subtends 70 degrees at the center?

• 140 degrees

• 70 degrees

• 105 degrees

• 35 degrees

What is the value of angle W in a cyclic quadrilateral if angle Z is 80 degrees?

• 100 degrees

• 90 degrees

• 80 degrees

• 180 degrees

What is the angle subtended at the circumference by an arc that subtends 120 degrees at the center?

• 90 degrees

• 60 degrees

• 120 degrees

• 30 degrees