Question

Q.9. in the given figure do&co are bisectors of angle ABC and angle BCD respectively. if angle ocd=30°, angle dab=100° and do =co. find the measures of angle doc angle adc angle abc

Answer 1

∠ DOC = 120°, ∠ ADC° = 60, ∠ ABC = 140°

Step-by-step explanation:

Given:

Here  DO and CO are bisectors of angle ABC

∠ OCD = 30°, ∠ DAB = 100°

Here OD = OC 

so ∠OCD = ∠ODC         [angle opposite to equal sides]

∠ ODC = 30°

So in Δ DOC,

using angle sum property of triangle

∠DOC +∠OCD + ∠ODC= 180

∠DOC = 180° − 30° − 30°

∠ DOC = 120°

Since DO and CO are the bisector of angle ADC and angle BCD,

so ∠ BCD = 2 ∠ OCD 

$\angle BCD = 2\times 30$

∠ BCD = 60°

And so is the ∠ADC = 2 ∠ODC 

$\angle ADC = 2\times 30$

∠ADC = 60°

and ∠ DAB = 100°                 [given]

So in quadrilateral ABCD, sum of all angle is 360 so

∠ ABC +∠ BCD +∠ CDA +∠ DAB = 360°

∠ ABC + 60° + 60° + 100° = 360°

∠ ABC + 220° = 360°

∠ ABC = 360° - 220°

∠ ABC = 140°

Answer 2

Step-by-step explanation:

DOC = 120°, ∠ ADC° = 60, ∠ ABC = 140°

Step-by-step explanation:

Given:

Here DO and CO are bisectors of angle ABC

∠ OCD = 30°, ∠ DAB = 100°

Here OD = OC 

so ∠OCD = ∠ODC [angle opposite to equal sides]

∠ ODC = 30°

So in Δ DOC,

using angle sum property of triangle

∠DOC +∠OCD + ∠ODC= 180

∠DOC = 180° − 30° − 30°

∠ DOC = 120°

Since DO and CO are the bisector of angle ADC and angle BCD,

so ∠ BCD = 2 ∠ OCD 

\angle BCD = 2\times 30∠BCD=2×30

∠ BCD = 60°

And so is the ∠ADC = 2 ∠ODC 

\angle ADC = 2\times 30∠ADC=2×30

∠ADC = 60°

and ∠ DAB = 100° [given]

So in quadrilateral ABCD, sum of all angle is 360 so

∠ ABC +∠ BCD +∠ CDA +∠ DAB = 360°

∠ ABC + 60° + 60° + 100° = 360°

∠ ABC + 220° = 360°

∠ ABC = 360° - 220°

∠ ABC = 140°