Question

Find the angles ABC,ADE,BCD in adjacent figure,where 'O' is centre of the circle.

Answer 1

angle abc plus angle adc equal to 180 (sum of opposite angles of quadrilateral incircle is 180 degree )
abc is equal to 110
dea is 90 dae is 60 hence ade will be 30
bad plus bcd is equal to 180 degree
dca is 90 degree cad is 20
bad plus bcd is 180
hence bcd is equal to 180 minus 50
that is 130

Answer 2

Answer:

Step-by-step explanation:

in triangle ADE,

angle AED = 90 (angle subtended by diameter in a circle on the circumference is always 90)

angle ADE+ angle AED + angle DAE = 180 (angle sum property)

ADE + 90 + 60 = 180

ADE + 150 = 180

ADE = 180-150 = 30

angle ACD = 90 (angle subtended by diameter in a circle on the circumference is always 90)

in triangle ACD,

angle ACD + angle ADC + angle DAC = 180 (angle sum property)

90 + 70 + DAC = 180

160 + DAC = 180

DAC = 180 - 160 = 20

in cyclic quadrilateral ABCD,

angle ABC + angle ADC = 180 (opposite angles in a cyclic quad. add upto 180)

ABC + 70 = 180

ABC = 180 - 70 = 110