Question

in the adjoining figure DO and CO are the bisector of ADC and BCD respectively. if ADC = BCD = 60° and DAB= 100° , find the measure of DOC , ADC and ABC. ​

Answer 1

Answer:

In △ADC, we have

∠DAC=60

0

and ∠ABD=50

0

By angle sum property, in △ABD

∠DAB+∠ABD+∠ADB=180

0

=>60

°

+50

°

+∠ADB=180

°

=>∠ADB=180

°

−110

°

=>∠ADB=70

°

We know that the angles subtended at the circumference by the same arc are equal.

∴∠ADB=∠ACB

=>∠ACB=70

0

Answer 2

Step-by-step explanation:

ADC = 60. (given)

In ΔDOC,

DOC + ODC + OCD = 180

DOC + 30 + 30 =180

DOC = 180 - 60

DOC = 120

ADC = 2 ODC

ADC = 2×30

ADC = 60

BCD = 2 OCD

BCD = 2×30

BCD = 60

In quadrilatal ABCD,

A + B + C + D = 360

100+B+60+60 = 360

B = 360-220

B = 140