Question

In circle P diameter QS measures 30 cm.

Answer 1

Given:

The diameter of the circle P is 30 cm.

The radius of the circle P is 15 cm.

The measure of ∠RPS is 125°

We need to determine the arc length of QR.

Measure of ∠QPR:

The angles QPR and RPS are linear pairs.

Thus, we have;

$\angle QPR + \angle RPS=180^{\circ}$

Substituting the values, we have;

$\angle QPR + 125^{\circ}=180^{\circ}$

          $\angle QPR =55^{\circ}$

Thus, the measure of ∠QPR is 55°

Arc length of QR:

The arc length of QR can be determined using the formula,

$Arc \ length =(\frac{\theta}{360})2 \pi r$

Substituting $\theta=55$ and r =15, we get;

$Arc \ length =(\frac{55}{360})2 (3.14)(15)$

$Arc\ length = \frac{5181}{360}$

$Arc \ length =14.4 \ cm$

Thus, the arc length of QR is 14.4 cm.

Hence, Option d is the correct answer.