An arc AB of a sector of a circle subtends an angle of 140° at the centre. Find the angle subtended at the 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. ∠ 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 = θ, where C is a point on the circumference. 140° = 2θ Step 4: Solve for θ. θ = (140°)/(2) = 70° The angle subtended by arc AB at the circumference is 70°.

An arc AB of a sector of a circle subtends an angle of 140° at the centre. Find the angle subtended at the 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. ∠ 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 = θ, where C is a point on the circumference. 140° = 2θ Step 4: Solve for θ. θ = (140°)/(2) = 70° The angle subtended by arc AB at the circumference is 70°.

Solved: An arc AB of a sector of a circle subtends an angle…

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.
$\angle \text{at center} = 2 \times \angle \text{at circumference}$
Identify the given angle at the center.
$\angle AOB = 140^\circ$
where $O$ is the center of the circle.
Let $\angle ACB = \theta$ , where $C$ is a point on the circumference.
$140^\circ = 2\theta$
Solve for $\theta$ .
$\theta = \frac{140^\circ}{2} = 70^\circ$
The angle subtended by arc AB at the circumference is $\mathbf{70^\circ}$ .

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

Step-by-step solution

Recall the circle theorem for angles subtended by the same arc.

Identify the given angle at the center.

Let $\angle ACB = \theta$ , where $C$ is a point on the circumference.

Solve for $\theta$ .

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More Mathematics Questions

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

Step-by-step solution

Recall the circle theorem for angles subtended by the same arc.

Identify the given angle at the center.

Let ∠ACB=θ\angle ACB = \theta∠ACB=θ, where CCC is a point on the circumference.

Solve for θ\thetaθ.

Still stuck on this one?

More Mathematics Questions

Let $\angle ACB = \theta$ , where $C$ is a point on the circumference.

Solve for $\theta$ .