Question

in the given figure abcd is a paralellogram if bp and cp are the bisectors of angle b and c the find angle bpc​

Answer 1

Step-by-step explanation:

In parallelogram ABCD,

opposite angles of parallelogram are equal

angle BAD=angle BCD=70

angle ADC=angle ABC

sum of all angles of a parallelogram is 360°,

BAD+ABC+BCD+ADC=360

70+ABC+70+ABC=360. (given above)

140+2ABC=360

2ABC=360-140

2ABC=220

ABC=110

now,

PB and PC are bisectors of B and C,

angle PBC=1/2 angle ABC

PBC=1/2*60

PBC=30°

angle PCB=1/2 angle BCD

PCB=1/2*110

PCB=55°

in ∆PCB,

sum of all angles of a triangle is 180°.

PCB+PBC+BPC=180

30+55+BPC=180

85+BPC=180

BPC=180-85

BPC=95°