An arc AB of a sector of a circle subtends an angle 140° at the centre of the circle. Find the angle subtended by the arc from the circumference.

Mathematics
An arc AB of a sector of a circle subtends an angle 140° at the centre of the circle. Find the angle subtended by the arc from the circumference.

ScanSolve AI Answer

Answer

7070^\circ

Step 1: Identify the central angle.
The chord AB subtends an angle of 140140^\circ at the center O of the circle.

Step 2: State the theorem.
The angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at a point on the remaining circumference:
θcenter=2×θcircumference\theta_center = 2 \times \theta_\text{circumference}.

Step 3: Set up the formula for the angle at the circumference.
θcircumference=12θcenter\theta_circumference = \frac{1}{2} \theta_\text{center}

Step 4: Substitute the given value.
θcircumference=12×140\theta_circumference = \frac{1}{2} \times 140^\circ

Step 5: Simplify.
θcircumference=70\theta_circumference = 70^\circ

Final answer: 70\boxed{70^\circ}

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Quick Answer

Identify the central angle. The chord AB subtends an angle of 140^ at the center O of the circle.

An arc AB of a sector of a circle subtends an angle 140° at the centre of the circle. Find the angle subtended by the arc from the circumference.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Identify the central angle. The chord AB subtends an angle of 140^ at the center O of the circle. Step 2: State the theorem. The angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at a point on the remaining circumference: _center = 2 × _circumference. Step 3: Set up the formula for the angle at the circumference. _circumference = (1)/(2) _center Step 4: Substitute the given value. _circumference = (1)/(2) × 140^ Step 5: Simplify. _circumference = 70^ Final answer: 70^