Question

in fig angle bac=85° ,ca=cb and bd=cd find the measure of angle x , angle y and angle z give reason to support your answer​

Answer 1

Answer:

70 degree

Step-by-step explanation:

In triangle ABC, o is the circumcenter and angle BAC=85 and angle BCA=75. What is angle OAC equal to?

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Given that in ΔABC , ∠BAC=85∘ & ∠BCA=75∘

∴∠ABC=180∘−∠BAC−∠BCA

=180∘−85∘−75∘

=20∘

Now, by property of chord of circle that the angle subtended by any chord at the center of circle is equal to double the angle subtended by the same chord at any point in the corresponding segment of circle,

∴∠AOC=2∠ABC=2(20∘)=40∘

Now, in isosceles ΔAOC , ∠OAC=∠OCA

∴∠AOC+∠OAC+∠OCA=180∘

40∘+2∠OAC=180∘(∵ ∠OCA=∠OAC)

∠OAC=180∘−40∘2

=70∘