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

PN is a straight line

So

∠ POT + ∠ TON = 180°

∠ TON = 180°-100°

∠ POT = ∠ CON = 100°

∠ POC = ∠ TON = 80°

According to the diagram

⇒ Taking point P & C of diameters

Minor arc = m(PWC) = 80°

Major arc = m(PYC) = 360°-80° = 280

⇒ Taking point C & N of diameters

Minor arc = m(CZN) = 100°

Major arc = m(CXN) = 360°-100° = 260°

⇒ Taking point N & T of diameters

Minor arc = m(NYT) = 80°

Major arc = m(NWT) = 360°-80° = 280°

⇒ Taking point P & T of diameters

Minor arc = m(PXT) = 100°

Major arc = m(PZT) = 360° -100° = 260°

PN & TC are diameters of circle

⇒ Taking diameter PN

Semicircular arc are PTN & PCN

m(PTN) = m(PCN) = 180°

⇒ Taking diameter TC

Semicircular arc are TPC & TNC

m(TPC) = m(TNC) = 180°