SATHEE: Quantitative Aptitude Ques 745

Quantitative Aptitude Ques 745

Question: The external bisector of $ \angle B $ and $ \angle C $ of $ \Delta ABC $ (where AB and AC extended to E and F, respectively) meet at point P. If $ \angle BAC=100{}^\circ , $ then the measure of $ \angle BPC $ is

Options:

A) $ 50{}^\circ $

B) $ 80{}^\circ $

C) $ 40{}^\circ $

D) $ 100{}^\circ $

Show Answer

Answer:

Correct Answer: C

Solution:

In $ \Delta ABC $ side AB and AC are produced to E and F, respectively and the external bisector $ \angle EBC $ and $ \angle FCB $ intersect at P. $ x+y+z=180{}^\circ $ $ y+z=180-x $ $ =180-100=80{}^\circ $ Now, $ 2\angle 1+y=180{}^\circ $ and $ 2\angle 2+z=180{}^\circ $

$ \therefore $ $ 2(\angle 1+\angle 2)=360{}^\circ -(y+z) $ $ =360{}^\circ -80{}^\circ =280{}^\circ $ and $ \angle BPC=180{}^\circ -(\angle 1+\angle 2) $ $ =180{}^\circ -140{}^\circ =40{}^\circ $

Quantitative Aptitude Ques 744

Quantitative Aptitude Ques 746

Quantitative Aptitude Ques 745

Question: The external bisector of $ \angle B $ and $ \angle C $ of $ \Delta ABC $ (where AB and AC extended to E and F, respectively) meet at point P. If $ \angle BAC=100{}^\circ , $ then the measure of $ \angle BPC $ is

Options:

Answer:

Solution:

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