Qeustion about inscribed angle in a circle.I have a circle as shown in the figure. In my text book, the angle BAD is the sum of angles ACD and angle ADC. There might be a theorem that shows this in the book but I cannot find it. Why is this true?

Question

dilettato5t1 · Accepted Answer

Since if slopes of lines are different, then they will intersect at some point, parallel lines must have the same slope.

Hayley Mcclain · Accepted Answer

Step 1  ∠  A  D  C  ≅  ∠  A  C  D, and by the triangle angle sum theorem and the figure   m  ∠  D  A  C  =      90    ∘  ,   m  ∠  A  D  C  =  m  ∠  A  C  D  =      45    ∘  .Step 2By the exterior angles theorem then,   ∠  B  A  D  =      90    ∘    =      45    ∘    +      45    ∘    =  m  ∠  A  D  C  +  m  ∠  A  C  D

I have a circle as shown in the figure. In my text book, the angle BAD is the sum of angles ACD and angle ADC. There might be a theorem that shows this in the book but I cannot find it. Why is this true?

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