Problem: Let the bisectors of the exterior angles at B and C of triangle ABC meet at D. Then, if all measurements are in degrees, angle BDC equals:
Answer Choices:
A. 21​(90−A)
B. 90−A
C. 21​(180−A)
D. 180−A
E. 180−2 A
Solution:
2∠b2∠c∴∠b+∠c But (∠B+∠C)∴∠b+∠c∠BDC​=180∘−∠B=180∘−∠C=180∘−21​(∠B+∠C)=180∘−∠A=180∘−21​(180∘−∠A)=180∘−(∠b+∠c)=180∘−(180∘−21​(180∘−∠A))=21​(180∘−∠A)​