Question

In Figure 6 oC and OD are bisectors of angle BCD and angle ADC respectively. If angle A=110°
find angle B​

Answer 1

Answer:

∠B=145°

Step-by-step explanation:

OD is bisector of CDA

∴CDA=CDO+ODA

=22.5+22.5(OD is bisector.so measure of both angles will be same)

CDA=45°

Similiarly

OC is bisector of DCB

∴DCB=DCO+OCB

=30+30(OC is bisector.so measure of both angles will be same)

DCB=60°

The given Figure is a quadilateral

∴∠A+∠B+∠C+∠D=360°(Sum of measures of angles of a quadilateral=360°)

110+∠B+60+45=360

215+∠B=360

∠B=360-215

∠B=145°

Answer 2

OC and OD are bisector

angle ADC =45degrees(bisector divides the angle in to two equal parts )

angle BCD=60 degrees (30×2)

sum of 4 sides of a four sides polygon is 360 degree

we know that 3 angles and their sum is 110+60+45=215

so angle B=360-215=145 degrees