Question

in figure if angle ADC =Angle CBP
Then prove that ABCD is cyclic​

Answer 1

Answer:

angle ABC + angle CBP = 180 .........angles in linear pairs

angle ABC = 180-angle CBP ......1

angle ABC = angle ADC ......given .......2

from 1&2

angle ADC + angle ABC = 180

by converse of cyclic quardilalateral theorem quardi.abcd is cyclic

Answer 2

The sum of opposite angles of a cyclic quadrilateral is 180°

Step-by-step explanation:

Given :∠ADC=∠CBP

To prove: ABCD is cyclic

Now as we know

∠ABC+ ∠CBP = 180° (linear pair ) ---(i)

Given that ∠ADC=∠CBP

substituting the value in (i)

we get

∠ABC+ ∠ADC = 180°  

∴ As the sum of opposite quadrilateral is 180° it is cyclic quadrilateral

Hence ABCD is a cyclic quadrilateral

# learn more

Prove opposite angles of a cyclic quadrilateral are supplementary

brainly.in/question/2373439