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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.

March 21, 2026Mathematics

ScanSolve AI Answer

Answer

70^\circ

5 steps

Identify the central angle.
The chord AB subtends an angle of $140^\circ$ at the center O of the circle.
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:
$\theta_\text{center} = 2 \times \theta_\text{circumference}$ .
Set up the formula for the angle at the circumference.
$\theta_\text{circumference} = \frac{1}{2} \theta_\text{center}$
Substitute the given value.
$\theta_\text{circumference} = \frac{1}{2} \times 140^\circ$
Simplify.
$\theta_\text{circumference} = 70^\circ$
Final answer: $\boxed{70^\circ}$

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