Angles in Circles

The video tutorial covers various theorems related to angles in a circle. It begins with the theorem that the angle subtended by an arc at the center is twice that at the circumference. It then explains reflex angles formed by major arcs and provides examples to find missing angles using these theorems. The video also discusses angles subtended by arcs in the same segment and concludes with the theorem that angles in a semicircle are right angles.

What is the relationship between the angle subtended by an arc at the center of a circle and the angle subtended by the same arc on the circumference?

• The angles are equal.

• The angle at the center is twice the angle on the circumference.

• The angle at the center is three times the angle on the circumference.

• The angle at the center is half the angle on the circumference.

What type of angle is always formed by a major arc at the center of a circle?

• Reflex angle

• Obtuse angle

• Acute angle

• Right angle

If a major arc subtends an angle of 120° at the circumference, what is the angle at the center?

• 60°

• 240°

• 120°

• 180°

In a circle, if angle AOC is 2a, what is the reflex angle AOC?

• 360° - 2a

• 180° - a

• a

• 2a

What is the sum of the interior angles of a triangle formed by points on a circle?

• 90°

• 180°

• 360°

• 270°

What is the theorem regarding angles subtended by an arc on the same segment of a circle?

• They are complementary.

• They are supplementary.

• They are reflex angles.

• They are equal.

If two angles are subtended by the same arc on the same segment, and one angle is 40°, what is the other angle?

• 80°

• 60°

• 40°

• 20°

What is the angle formed in a semicircle?

• Obtuse angle

• Right angle

• Reflex angle

• Acute angle

If PSQ is a diameter of a circle, what is the angle subtended by any point on the circle?

• 60°

• 90°

• 45°

• 180°

In a circle, if the diameter is AC and an angle is subtended from the diameter, what is the measure of this angle?

• Obtuse angle

• Right angle

• Acute angle

• Reflex angle