How to find an angle?

[marinaa11]

Hi, I'm struggling with this task: find an angle D of the BDC triangle.
information given: the angle B (of triangle ABC) = 65 , the angle C (of triangle ACB) = 35.
My solution: I got that angle A is 80 (180-65-35), but don't know, that's next...
Thank you for help.

 

[Deleted member 4993]

Hi, I'm struggling with this task: find an angle D of the BDC triangle.
information given: the angle B (of triangle ABC) = 65 , the angle C (of triangle ACB) = 35.
My solution: I got that angle A is 80 (180-65-35), but don't know, that's next...
Thank you for help.

View attachment 22533

Have you been taught any "circle" theorem? Particularly:

All angles inscribed in a circle and subtended by the same chord are equal. The inscribed angle is equal to one half of the central angle subtended by the chord.

 

[marinaa11]

I got it, thank you

 

[pka]

Hi, I'm struggling with this task: find an angle D of the BDC triangle.
information given: the angle B (of triangle ABC) = 65 , the angle C (of triangle ACB) = 35.
My solution: I got that angle A is 80 (180-65-35), but don't know, that's next...
Thank you for help.

View attachment 22533

Please note that \(\angle A~\&~\angle D\) both are inscribed angles and both intercept the arc \(\widehat{BC}\).
What does that tell us about their measures?

 

[marinaa11]

Please note that \(\angle A~\&~\angle D\) both are inscribed angles and both intercept the arc \(\widehat{BC}\).
What does that tell us about their measures?

Does what mean that angle D is equal to angle C?

 

[pka]

Does what mean that angle D is equal to angle C?

If you say that angle D equals angle C that means they are exactly the same angle!
From the diagram they are clearly different angles.
Do you mean that they have the same measure? The answer is not necessarily.
It does mean \(m(\angle A)=m(\angle D)=80^{ \circ}\).

 

[marinaa11]

If you say that angle D equals angle C that means they are exactly the same angle!
From the diagram they are clearly different angles.
Do you mean that they have the same measure? The answer is not necessarily.
It does mean \(m(\angle A)=m(\angle D)=80^{ \circ}\).

Finally, I understood! Thanks a lot