Question

In
figure PORS
in cyclic side PQ=~ side RQ,
LPSR = 110 Find
MLPOR,M(arc OR)
​

Answer 1

Answer:

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

⇒∠PSR+∠PQR=180°

⇒∠PQR=180°

−110°

⇒∠PQR=70°

(2) 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°

{Using Measure of a major arc = 360°

- measure of its corresponding minor arc}

(3)side PQ≅ side RQ

∴m(arcPQ)=m(arcRQ) {Corresponding arcs of congruent chords of a circle (or congruent circles) are congruent} ⇒m(arcPQR)=m(arcPQ)+m(arcRQ)

⇒m(arcPQR)=2×m(arcPQ)

⇒m(arcPQ)=110°

(4)In △PQR,

∠PQR+∠QRP+∠RPQ=180°

{Angle sum property}

⇒∠PRQ+∠RPQ=180°

−PQR

⇒2∠PRQ=180°

−70°

{∴sidePQ≅sideRQ}

⇒∠PRQ=55°