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

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

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Answer

2×∠at circumference2 \times \angle \text{at circumference}

Step 1: Recall the circle theorem for angles subtended by the same arc.
The angle subtended by an arc at the center is twice the angle subtended at the circumference.

∠atcenter=2×∠atcircumference\angle at center = 2 \times \angle at circumference

Step 2: Identify the given angle at the center.

∠AOB=140∘\angle AOB = 140^\circ

where OO is the center of the circle.

Step 3: Let ∠ACB=θ\angle ACB = \theta, where CC is a point on the circumference.

140∘=2θ140^\circ = 2\theta

Step 4: Solve for θ\theta.

θ=140∘2=70∘\theta = \frac{140^\circ}{2} = 70^\circ

The angle subtended by arc AB at the circumference is 70∘\mathbf{70^\circ}.

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Recall the circle theorem for angles subtended by the same arc. The angle subtended by an arc at the center is twice the angle subtended at the circumference.

An arc AB of a sector of a circle subtends an angle of 140° at the centre. Find the angle subtended at 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: Recall the circle theorem for angles subtended by the same arc. The angle subtended by an arc at the center is twice the angle subtended at the circumference. at center = 2 × at circumference Step 2: Identify the given angle at the center. AOB = 140^ where O is the center of the circle. Step 3: Let ACB = , where C is a point on the circumference. 140^ = 2 Step 4: Solve for . = (140^)/(2) = 70^ The angle subtended by arc AB at the circumference is 70^.