Question

PQRS is cyclic mZPSR = 110° then find
a)
mZPQR
Р
b)
m(arc POR)​

Answer 1

Answer:

a. Given PQRS is a cyclic quadrilateral. ∴ Opposite angles of a cyclic quadrilateral are supplementary

⇒∠PSR+∠PQR=180

⇒∠PQR=180 -110

⇒∠PQR=70

b. 2×∠PQR=m(arcPR){The measure of an inscribed angle is half the measure of the arc intercepted by it.}

m(arcPR)=140

⇒m(arcPQR)=360

−140

=220

o

{Using Measure of a major arc = 360

- measure of its corresponding minor arc}