Question

In the figure, seg PN and seg TC are the diameters of a circle. Write the measures of the arcs formed by the end-points of these diameters and explain your answers.

Answer 1

Measure of the central angle is 100°.
$$\begin{gathered} \angle POT=100°\left(\mathrm{Given}\right) \\ \angle CON=\angle POT=100°(\text{V}\mathrm{ertically}\mathrm{opposite}\mathrm{angle}) \\ \angle POC=180°-100°=80°(\mathrm{Linear}\mathrm{pair}) \\ \angle TON=\angle CON=80°(\text{V}\mathrm{ertically}\mathrm{opposite}\mathrm{angle}) \end{gathered}$$
∴ Minor arc:
m(arc CZN) = 100°
m (arc PWC) = 80°
m(arc TYN) = 80°
m(arc PXT) = 100°
Major arc:
m(arc PZT) = 360° $-$100° = 260°
m (arc CXN) = 360° $-$100° = 260°
m(arc PYC) = 360° $-$ 80° = 280°
m(arc TWN) = 360°$-$80° = 280°