Question

IN the given figure,'DO' and 'CO' are the bisectors of angle ADC and angle BCD respectively. If angle ADC = angle BCD = 60 degree and angle DAB =100 degree. Find the measure of angle DOC and angle ABC. The intersecting point is 'O'.

Answer 1

hope this helps.....

Answer 2

The measure of ∠DOC us 120° and ∠ABC is 140°

GIVEN

'DO' and 'CO' are the bisectors of ∠ADC and ∠BCD respectively. If ∠ADC = ∠BCD = 60° and ∠DAB =100°.

TO FIND

∠DOC and ∠ABC.

SOLUTION

We can simply solve the above problem as follows;

We know that,

CO is the angle bisector of ∠BCD

Therefore,

∠BCO = ∠OCD = 1/2 ∠BCD

∠ODC = ∠OCD = 30°

In ΔOCD

∠OCD + ∠COD + ∠CDO = 180° (sum of interior angle of triangle)

30 + ∠COD + 30 = 180

∠COD = 180 - 60 = 120°

In quadrilateral ABCD

∠A + ∠B + ∠C + ∠D = 360° (sum of angles of a quadrilateral)

100 + ∠B + 120 = 360

∠B = 360-220 = 140°

∠ABC = 140°

Hence, The measure of ∠DOC us 120° and ∠ABC is 140°

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