Question

in the given figure PO and CO are the bisector of angle ECB respectively if angle BAC = 50 and angel ABC = 60 then find angel BOC​

Answer 1

Answer:

<BOC = 65°

Step-by-step explanation:

GIVEN THAT:-

<ABC=60

we know that PBA forms a straight line therefore <PBC is 180°

Therefore <ABC+<PBC =180°(Angle PBA)

<PBC=180-60

<PBC=120°

Given that BO is the bisector of angle PBC

Therefore <PBO = <CBO

<PBO+<CBO=<PBC

2<CBO=<PBC(120°) {substituting PBO in the place of CBO}

CBO=120/2

CBO=60°

By angle sum property

<ABC+<BCA+<CAB=180°

60°+<BCA+50°=180°

<BCA=180-110

<BCA=70°

In the same procedure used in finding angle CBO we will find angle BCO

180-70=110

110/2 = 55°

<BCO = 55°

By angle sum property

<CBO+ <BOC+ <BCO =180°

60+<BOC+55=180

<BOC= 180-115

<BOC=65°