Reflex Angle Calculation
The angle subtended by the arc AB at the center is given. We need to find the reflex angle formed by the same arc at the center.
- A full circle has a total angle of $360^\circ$ around the center.
- The angle subtended by arc AB at the center is given as $140^\circ$.
- The reflex angle is the angle larger than $180^\circ$ covering the rest of the circle.
Calculating Reflex Angle for Arc AB
To find the reflex angle, subtract the given angle from the total angle of a circle ($360^\circ$).
- Given angle = $140^\circ$
- Total angle = $360^\circ$
- Reflex angle = Total angle - Given angle
- Reflex angle = $360^\circ - 140^\circ$
- Reflex angle = $220^\circ$
Therefore, the reflex angle made by arc AB at the center is $220^\circ$.
Similar Questions
- When a transversal intersects two parallel lines, one of the alternate interior angles is 115°. What is the measure of the angle that lies opposite to it on the alternate interior side?
- Two angles are complementary. The measure of one angle is 10 degrees more than three times the measure of the other angle. What is the measure of the smaller angle?
- In a right triangle, one of the acute angles is $30^\circ$. What is the measure of the exterior angle at the right-angled vertex?
Two parallel lines are intersected by a transversal. If a pair of corresponding angles is formed, and one of the angles measures 130°, what is the measure of the other angle?
Important Questions from Lines and Angles
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is:
The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?
In a ΔABC, the bisectors of ∠B and ∠C meet at point O, inside the triangle. If ∠BOC = 122°, then the measure of ∠A is:
In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?
