如图,△ABC中,AB=AC,∠A=50°,P是△ABC内一点,且∠PBC=∠PCA,则∠BPC的度数等于( ) A.100° B.115° C.130° D.140°
问题描述:
如图,△ABC中,AB=AC,∠A=50°,P是△ABC内一点,且∠PBC=∠PCA,则∠BPC的度数等于( )
A. 100°
B. 115°
C. 130°
D. 140°
答
∵AB=AC,∠A=50°,
∴∠ABC=∠ACB=65°.
∵∠PBC=∠PCA,
∴∠BPC=180°-(∠PBC+∠PCB)=180°-(∠PCA+∠PCB)=180°-∠ACB=115°.
故选B.