Question

Find the value of angle AOD?

Answer 1

Step-by-step explanation:

AOD - since it forms a triangle and the sides of the triangle are radius of circle they are equal so ADO = DAO. to find AOD: 180⁰-36⁰-36⁰=108⁰.

ODC - first we find DOC :180⁰-108⁰=72⁰.since the other 2 sides of the triangle are equal we can find ODC by : 180⁰=72⁰+2x

2x=180⁰-72⁰

2x=108⁰

x=108⁰/2

x=54⁰

the other 3 right now i dont have an idea but if i think of it later i will comment it here.

ABC -its 120⁰ because it forms Z angles with CEF

CFD -first we find ODE which we do by : 90⁰-54⁰=36⁰. Then we find CED by : 180⁰-120⁰=60⁰.Then we find DCE by: 180⁰-36⁰-60⁰=84⁰.Then we find ECF by :180⁰-54⁰-84⁰=42⁰.And now we find CFD by : 180⁰-120⁰-42⁰=18⁰.

CAB -first we find BCA by : 180⁰-54⁰-84⁰=42⁰ or you can say it is equal with ECF because they are opposites of the same point.Then to find CAB we : 180⁰-120⁰-42⁰=18⁰ or you can say it is equal to CFD because they form Z angle.