What is the angle subtended on the major arc of a circle?

What is the angle subtended on the major arc of a circle?

Theorem: The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle’s circumference. If the two opposite interior angles happen to be equal, then the exterior angle will be twice any of the opposite interior angles.

What is the angle subtended at the Centre of a circle of radius 5 cm by an arc length 4 cm?

144° is the answer .

What is a subtended arc?

In geometry, an angle is subtended by an arc, line segment or any other section of a curve when its two rays pass through the endpoints of that arc, line segment or curve section. We also sometimes say that an arc is intercepted or enclosed by that angle. The precise meaning varies with context.

What is the angle subtended at the centre of a circle of radius 6cm?

Answer: The angle subtended at the centre of the circle is 90° .

What is the angle subtended at the centre of circle of radius 6cm by an arc of length 3πcm?

What is the angle subtended at the centre of a circle of radius 5cm by an arc?

Radius (r) = 5 cm. θ = angle subtended at centre (degrees) Length of Arc = θ/360° x 2πr cm. But arc length = 5π/3 cm. Therefore, Angle subtended at centre = 60°

What is the angle subtended at the centre of a circle of radius 10 Centimetre by an arc of length 55 cm?

∴ the angle subtended at the centre of a circle is 90°.

What is the measure of the subtended arc in units of 1/4 of the circle’s circumference?

The circumference of the entire circle is (2 π r); the arc length of the 1/4 of that circle subtended by this angle is L = (2 π r) / 4 = (π r) / 2; and the ratio of that arc length L to the radius r is π / 2. So 90° = π / 2 radians.

Which arc is a major arc?

180 degrees
An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.

What is angle subtended by diameter?

The diameter of a circle subtends an angle of 90∘ at any point on circle. So the angle is 90∘.

What are subtended angles in a circle?

In a circle, there are various angles that can be formed joining the endpoints of arcs and those angles are termed subtended angles. There are different categories of angles formed by these arcs, for example, angles in the same segment, angles in a semi-circle, angles at the circumference, etc.

What does it mean if an arc subtends a part?

Posted 8 years ago. Direct link to Ben Willetts’s post “If an arc subtends a part…” If an arc subtends a particular angle at the centre of the circle, it means that if you draw straight lines from each end of the arc to the centre of the circle, that’s the angle you get between the two straight lines.

How to find the value of angle subtended by an arc?

To find the value of angle subtended by an arc at the center we have to multiply the angle formed through the same end-points of the arc on the circumference by two. For example, if the angle subtended at any point on the circumference is 60 º, that means the angle subtended by the same arc at the center is 120 º .

What are the rules for congruent arcs?

Important Notes: 1 Congruent arcs of a circle subtend equal angles at the center. 2 The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. 3 Angles in the same segment of a circle are equal. 4 An angle in a semicircle is a right angle.