given: B=63, C=54 prove A=63

Question

it is a triangle 

Answer 1

The three angles of a triangle add to 180º.

 

If angle B=63º and angle C=54º, then the third angle, angle A, must be 180º-63º-54º=63º.

 

Now, if you must also prove that the three angles sum to 180°, take the "Turtle Graphics" (a.k.a., Logo) approach and say that from point A going to point B, the line turns (180º-Bº), then proceeds to point C, where it turns (180º-Cº), then proceeds to point A again, where it turns (180º-Aº) to be a total of 360º to point in the initial direction again.  These angles add up to:  (180º-Bº)+(180º-Cº)+(180º-Aº) = 540º-(Bº+Cº+Aº) = 360º.  So, (Aº+Bº+Cº)=180º.